Regarding 1960, is there a realistic chance that Texas was stolen? The margin for Kennedy in Texas was about the same (in percentage terms) as Bush's margin in Ohio in 2004. Seems to me that Republican sour grapes about 1960 makes as much sense as Democrats claiming that 2004 was stolen.
Nixon needed Texas as well as Illinois to win, remember (some people claim that Mayor Daley stole the entire election for Kennedy; clearly not true, as Kennedy would have still won even if Illinois went for Nixon).
I agree that there should have been a full manual recount of the entire state. It's important to remember, however, that Bush opposed this. My guess is that Gore thought that since Bush was opposing a full recount, due in large part to the argument that it would be too expensive and too time-consuming, he thought maybe suggesting a smaller recount would be a good idea. Of course, the fact that he picked Democratic counties to count probably isn't just a coincidence, but still, it's important to remember that Bush opposed a full manual count, and it would have been hard for Gore to get one.
During Johnson's first run for the Senate, he was expected to get trounced by his primary opponent. He gained a lot of votes through his campaign style, but it is nearly impossible for him to have won without massive, wide-spread cheating... massive. Probably enough to shift the vote 7%-10%! Those same people ran the Kennedy campaign in Texas in 1960 and turnout patterns were, uhhh... abnormal, to say the least.
Johnson's win in a 1941 ('42?) Democratic primary was stolen, and consequently he made sure that his Senate seat would not be stolen again. I agree his 1948 win in the Democratic primary was stolen, but his future re-elections to the Senate from Texas were massive, and I doubt that the Texas results in the 1960 election were stolen, unless someone has any information that would lead me to conclude otherwise.