Ok, even accepting the premise as a whole, why does Shepherd in the future look the same in the final scene as he did the first time John met him? They'd changed the timeline so that he had to fake his death and go on the lamb 30 years earlier. He shouldn't be clean-shaven, and wearing a nice suit. He probably just spent 30 years in the criminal underworld.
It's entirely possible for someone to hide in plain sight, with a respectable job which involves wearing a suit (they said he'd been a private detective after leaving the police force, so it could be that). Faking his death means the police wouldn't be looking anyway.
In the pilot, the first call happens on October 21, and Raimy predicts a double homer for the third game of the 1996 World Series. Time is supposedly running in parallel. Frank cannot confirm this prediction until the night of the 22nd, when the game is played. He makes another call, with the burn mark happening, that night, and hangs up on the call with a threat not to call again. It isn't until the next day, after a coffee can test message, that Raimy calls back and tells him "You die tomorrow. October 23, 1996, game four of the Series." and Frank says, "Tomorrow night... tomorrow night where?" Somehow they added a whole extra day between October 22 and October 23.
The pilot as released on Netflix makes an attempt to fix this, by captioning Raimy's birthday in 1996 as October 20, and the next day as October 21. However, the tie-in to the World Series makes this fail.
Another big one: was Frank using his ham radio from his undercover location, or from the family garage? If the former, how did it get back to his garage in order for young Raimy to get a call from older Raimy, and take it to the hospital after he was shot? If the latter, wasn't that a huge risk to his cover?
I get why they spent their efforts trying to find the Nightingale, to save Julia and the other victims. But couldn't Raimy take five minutes to tell Frank how to not get killed in his 2011 car crash? She mentions it, but no specific date, so he could call in sick or something.