I think this is just differing perspectives; a lot of what you highlight, for me, makes US sports unwatchable (as i said elsewhere I can't watch all of a baseball game simply through boredom - despite quite liking the game).
(though for the record post-mortems, referee training etc. are good ideas)
Referees should be required to make distinguishing hand signals for each call. This would greatly aid the players, the fans, and the commentators in determining exactly what the ruling was.
This is the case - hand signals are pretty conclusive in Football (and relatively simple).
Offsides should always be "tie goes to the offense".
Ouch, no. You'd see far too many goals scored like this; in fact from my observation the way it comes out if "tie could go both ways" - which makes it all the more fun/difficult to play. And more importantly keeps it relatively fair. I dislike sports that are "binary" - i.e. if it's A it's A. In football sometimes it is A but the ref calls B.
For minor fouls in the box on set pieces, there should be discretionary power to the referee to retake or reverse the direction of the kick instead of either calling a game altering PK or doing nothing (and thus providing an incentive for questionable behavior in the box). There's simply insufficient granularity there. Minor defensive holding should generate a warning and another kick from the same spot for another scoring chance (but at a much lower scoring percentage than PK).
See this is what frustrates me about US sports... it starts to get complicated. There is no need to introduce this complexity because the game is already well defined and correctly played in this area.
If a player leaves the field of play for an injury, or is down for more than 1 minute, the player should not be able to return for 5 minutes.
This just demonstrates, IMO, a misunderstanding of the game. 5 minutes may be no time in, say, American Football. In Football the game could be entirely changed in 5 minutes.
I think the biggest problem is that compared to many US sports Football is an extremely fast moving game that relies on being able to run smoothly and cohesively. For example if the ball goes out of bounds it could easily be thrown back in within just a few seconds and the momentum of the game continues (for me this is what I enjoy most).
There is, obviously, a culture difference. I think that is why I find US sports quite boring and unwatchable and some Americans want to change/slow/formalise football. I think... each to our own thank you :)
In my mind football is a perfect spectator sport because of the "flaws" introduced by human error. They make a game less predictable, more excruciating, provide human emotion etc.
(although I do think the current crop of players are a bunch of spoiled brats and need to be reminded of the real game)