Ok, notes for AoS Season 3:
3x01 has no specific time references in terms of time passed between 2x22 and 3x01, but we can figure that out due to 3x05 "4,772 Hours" being a little over 6 and a half months. Backtracking a bit from there (to cover time passed during 3x01-3x04) places 3x01 around 6 months after 2x22, so October 2015. Bobbi mentions there's been no new reading on the Monolith in "months". Bobbi is still also doing rehab for her knee injured in 2x21/2x22. Fitz also mentions he tracked the parchment that has info on the Monolith to Mosul Central Museum in Iraq, until the museum was taken over by "your extremist buddies when they ransacked the place this year". This is a reference to ISIS/ISIL, who occupied it in 2014 but in February 2015 (around 8 months before this episode occurs) the terrorists began burning books and destroying artifacts. This is likely what Fitz is referencing. Coulson also mentions the "Pym Technologies disaster", a reference to ending of Ant-Man, which occurred in early October, 2015. Presumably AoS 3x01 picks up in middle or late October.
3x02 picks up immediately after 3x01, literally seconds later. Coulson gives a vague "its been months" comment regarding Simmon's disappearance into the Monolith. At the 7:07 mark, Ward is getting out of a convertible in a parking garage, and sticker on the car window shows registration expiration of 10/2015, which is that month. Garner says Joey won't be ready for field work for at least 3 months, so presumably Joey's first mission in 3x09 "Closure" happens around 3 months later, course that depends on if the episodes follow on after the other with no break points. The aerial establishing shot at 41:24 shows mostly green trees, but a few changing color to brown, red, or yellow, indicating Fall is in swing, which lines up with October setting for the early episodes. Werner von Strucker (posing undercover as a student) asks Garner if he'd be able to sign up for/add his class, and Garner asks if he's "ok with a few weeks of make-up work", indicating the semester started a few weeks before, which lines up with September, maybe late August, when Fall semester college courses usually start in US.
3x03 picks up the next day after 3x02, as second scene shows the team discussing Simmons lab tests after returning from Maveth at end of 3x02. Simmons is also still sensitive to light and sound, indicating she only just returned. At the 5:35 mark, an establishing shot of the bar Hunter and May are in has a bunch of pumpkins lined up on stairway to left of the bar, and a corn stalk decoration around tree in front. This likely indicates its October, possibly November, but October is likelier since the previous episodes, which this one immediately follows, also occur in October. A banner inside the bar reads "Boston Red Socks Gameday Special" (anyone from Boston knows its spelled Red Sox, so guess the prop department dropped ball on that one). Regardless, it shows its during MLB season, which runs from April to October (regular season) and October to November for playoffs and World Series. The Red Sox had a crappy year in 2015 so didn't make it to playoffs, and their last game that year was on October 4. That doesn't really line up with the timeline of the MCU, since 2x22 occurred likely in early to mid April, and Simmons was on Maveth for over 6 and a half months (198 days), which would put the timeline around mid October, maybe even late October (which would account for the Harvest/Fall decorations outside the bar). We'll chalk that discrepancy up to MCU being different timeline than our own. Perhaps the Red Sox made it to the playoffs in the MCU reality in 2015.
3x04 picks up likely not long after 3x03, as Bobbi asks Fitz about him and Simmons having dinner. Mack also mentions the ATCU were after Daisy "the other day", which occurred in 3x03. Ward's henchman mentions the fight that Hunter got into with Spud to infiltrate Hydra happened "last week". Since there's a week span I'll use that to push 3x04 to November.
3x05 (the present day framing portions) picks up immediately after 3x04.
3x06 picks up immediately after 3x05. Garner mentions Strucker signed up for his class (which happened at end of 3x02) "a few weeks ago".
3x07 picks up immediately after 3x06.
3x08 picks up very soon after 3x07, likely the next day, as Garner is being transferred into ATCU custody (after being captured at end of 3x07). Lincoln also mentions "last night" was first time he'd slept well in awhile, due to being on the run, and he only joined the team in the previous episode. Rosalyn mentions she couldn't check her fantasy football scores due to them blocking reception on her phone, confirming this episode occurs sometime during NFL (or College) football season which ran from September to January, and playoffs during January, 2016. This aligns with episode occurring likely in November, 2015.
3x09 picks up sometime after previous episode. Its indeterminate exactly how much, but likely not too long, a week or two maybe. It allows a slight break point, or possibly even enough to push into January, 2016, if necessary (depending on how rest of season works out).
3x10 picks up immediately after 3x09.
3x11 picks up sometime after 3x10, presumably a month or so due to the "3 months from now" tag at beginning of episode which showed scene from 3x22, placing 3x11 in January, 2016.
3x12 picks up not too long after 3x11, but could be a week or two. Either way its a possibly break point in terms of moving up a month. Malick makes mention that Ward's body isn't improving/healing, indicating at least some time (maybe a few weeks) has passed since he came to Earth through the portal at end of 3x10. Simmons analyzes a sample of Daisy's blood "taken two years ago before she was exposed to Terrigen". That aligns with it occurring sometime between Season 1 and 2, during the winter Talbot pursed the team.
3x13 picks up soon after 3x12, presumably not long after Malick's plane landed, and the episode covers a day and a half. The interrogator mentions its the "dead of winter", likely indicating its January or February. Hunter mentions events of 2x18 "The Frenemy of My Enemy" as occurring "last year". That works, as 3x13 is in at least February, 2016, and 2x18 occurred just before Age of Ultron in April, 2015, so its around ten months actual time, and certainly fulfills the "last year" dialogue since it was early 2015, and its early 2016 when Hunter says this.
3x14 picks up an indeterminate amount of time after 3x13. Opens with shot of motorcycle license plate which expired Jan 2016, which may be when this episode occurs. Mack mentions Bobbi and Hunter leaving SHIELD was recent, so presumably this is within a week or two max. Daisy mentions "Damage Control will clean up" the scene.
3x15 picks up an indeterminate amount of time after 3x14, but not too long after as its said Mack is still recovering from his gunshot wound (that he got in 3x14). Most likely a week or so at most between the episodes.
3x16 picks up not long after 3x15, likely the next day since Malick is returning home, and Coulson is still obsessing over Ward's return as Hive. Coulson also tells May he's sorry about Andrew (his final transformation into Lash), so that likely happened day before at most as well. Daisy's facial lacerations from her fight with Malick previous episode are still fresh, and Fitz and Simmons are examining the skeletons of the board members of Transia Corp that Ward/Hive killed in previous episode. All signs show this as picking up next day after 3x15.
3x17 picks up immediately after 3x16. A note on the flashback to Alveus creation: Coulson mentions "all the ancient Satanic creation myths, they were based on him". That implies Alveus/Hive's metamorphosis into an Inhuman occurred pre-New Testament days.
3x18 picks up the next day after 3x17, with the team fixing up base. Fitz confirms this by mentioning his and Simmon's hookup happened "last night".
3x19 picks up sometime after 3x18, long enough for Radcliffe to have gotten his process up and running (maybe a few days).
3x20 picks up an indeterminate amount of time after 3x19. Not long, as Lincoln mentions he's been in quarantine for "days". Also of note, Peggy is shown to be 95 years old at the time of her death. She was born April 9, 1921 and her 95th birthday would be April 9, 2016. Her funeral is held on April 10, 2016, so presumably she died on her birthday and funeral was set up quickly (not unlikely if she'd been sick for awhile and her death was expected, not to mention her high prominence in SHIELD/British government). Coulson's leg is still healing from the injury sustained in 3x18, so its not too long after that episode. Daisy's facial lacerations (from 3x16) are also finally almost healed. Mack's broken bones (sustained by Daisy in 3x19) are also healing.
3x21 picks up not long after 3x20. A technician tells Fitz parts for the hangar door (which was damaged at end of 3x17 by Daisy under Hive's control) were delayed "for a few days", indicating it hasn't been too long since then.
3x22 picks up immediately after 3x21.