Time dilation would explain how the mysterious woman doesn't age between her appearances in Haven. It would also explain Lexie DeWitt's experiences in the Barn. For DeWitt, time moved in an unusually compressed fashion-she'd think that she'd gone home, had dinner, slept and come back to work, but in reality no time had passed at all and these were just more Fake Memories. When DeWitt became aware that things were not what they seemed to be, this stopped fully affecting her and she became aware that time was passing differently.
The Barn's time travel also appears to be at least somewhat controllable. According to Agent Howard it came whenever the mysterious woman called it.[note 3] Howard is also able to use The Barn to travel to Haven outside of the 27-year cycle.
Anson Shumway's Trouble traps Parker in a Groundhog Day Loop. Shumway is the only Troubled person with the ability to affect time was does not have a ripple-effect-proof memory. Parker not only has a ripple-effect-proof memory, but seems to be reset-button-proof as well. Unlike other people who's injuries and deaths reset when the day starts over again, Parker's body retains all the wear and tear it went through. When she wakes up on the day the loop ends, she's already been awake for 17 hours and 44 minutes and has injuries from the previous loops.
While not strictly time travel, Hadley Chambers' Trouble invokes Ret Gone as she makes everyone in Haven disappear one-by-one, leaving the remaining Havenites with no memory of their ever existing. The HPD class photo, the Haven Herald subscription list and the "Welcome to Haven" sign function as Ripple Effect Indicators. Unlike the alternate universes created by other Troubles, where everything resets if the Trouble person dies, the Chambers Trouble seems to actually have Ontological Intertia. When Arthur Chambers committed suicide, the people his Trouble erased did not return. However it's unknown if Arthur Chambers committed suicide *after* the Troubles left, something that may have given the world he created permanence.
When Cliff's wife, Susie, dies, his Make a Wish Trouble is activated and he wished for a Haven without the Troubles, one where Susie would still be alive. In classic Be Careful What You Wish For fashion, his wish creates an Alternate Universe where Haven has never been plagued by the Troubles. Unfortunately, that also means that while Susie is still alive, she's married to someone else.
In this Troubless Altverse, Haven is no longer "Haven to God's orphan's" but "The safest town in Maine", a town that hasn't has a murder in 42 years. Duke Crocker is not a criminal, but third-generation HPD Detective. Max Hansen was never a violent criminal and so Nathan Wuornos never existed—a happily married doctor, Nathan Hansen exists in his stead. Garland Wuornos did not become a cop. Vince and Dave Teagues still accumulated enormous wealth but did not need to resort to illegal means to hide it. While Troubless Haven does have major differences, it's largely a universe based on the principle of In Spite Of A Nail, mainly because it's an exercise in What If?.
People immune to the Troubles (the mysterious woman and William) have Ripple-Effect-Proof Memories and are able to notice that the world around them has changed. Sometimes the person who's Trouble is changing things also has a ripple-effect proof memory. Hadley Chambers is able to remember the people she's erased and Cliff is able to remember the Haven that used to be.
The Chambers Trouble leaves lots of Ripple Effect Indicators lying around. Some of these are only obvious to people with ripple-effect-proof memories: the changing population numbers on the "Welcome to Haven" sign and editions of the Haven Herald. Some of these are noticeably odd to everyone: abandoned cars, a several hundred page delivery list with with only a handful of names, a police station with dozens of desks for two cops.
Things created by the Troubles require the Troubled person's continued existence, to the extent that even alternate universes created by a Trouble have No Ontological Intertia; if the person who's Trouble caused the timeline change dies, the new timeline ends too. This means that most deaths in these alternate universes are generally subject to a Reset Button.[note 9] However a person immune from the Troubles who gets injured or killed in an alternate universe is in unusual peril because they would stay dead once the Trouble ended and the timeline was restored.[note 10] The Troubled person causing the changed timeline is also in particular peril. Shumway and Cliff both die in order to stop their Troubles and their deaths are the only deaths that carry over into the real timeline. Whether this is a side-effect of immunity to the Troubles/causing the Troubles or because Your Mind Makes It Real is unknown.
↑Weirdness search and rescue is later invoked during their trip to rescue Parker from the Barn.
↑Crocker's gold dubloon exists only between August 16th 1955 when he arrives in the past and late 2010 when he's sent back. Try not to think about it too hard, it'll give you a headache.
↑Duke gets sent back to the past by going to see Stuart Mosley after reading his name in the Crocker journal. But the Guard only knows about Mosley and only orders Roy Crocker to kill him after overhearing a conversation between Nathan and a Guardsmen.
↑The world of Haven following multiple temporal mutability standards may be justified by Parker's immunity to the Troubles. Mosley's Trouble creates a Reverse Grandfather Paradox but her immunity lets her see Haven as it would be without this paradox.
↑Wuornos assumes that William tracked down Cliff and murdered him again in order to keep his Trouble from being re-triggered, but the writers have confirmed that Cliff's AU death carried over.
↑The Chambers Trouble may be an exception to this rule. See #Ret gone.
↑As the writers have not killed off Parker or William permanently, and as they can't kill them off permanently more than once, this is an assumption. However Parker's injury during the Groundhog's Day loop survived multiple resets as did her change of clothes in "The Trouble With Troubles".
↑When Parker wakes up in the Troubleless altverse, she has not been moved physically. She went to bed in her apartment above The Grey Gull and woke up on the floor of a storage room above JoJo's Bait Shop, which had replaced the Gull in the altverse. When Cliff is killed though, she's moved across town, and wakes up back in her bed. No explanation is given for this.