Is he really that bad? Subtract Bran, and his plan works pretty well. But in the end he got outplayed by a guy who somehow became a walking WeirwoodPedia. (Well not the walking part.) No one could have foreseen that.
Yes!
The ned thing was in a throne room with a bunch of visitors, also Cersei could have talked at any point. Vy the way, that event is 6 years ago.
The lysa murder sansa knew about, lied to royce about it and ignored it. Again, 4 years ago.
Littlefinger should have calculated those two things being known and should have prepared plausible excuses/planned accordingly.
Also, it wasn't too far fetched that Sansa/Arya might talk about the issue and it's quite terrible to have no possible reaction in that eventuality.
The Jon Arryn murder accusal was obviously undefendable except for outright denial (I mean, there is no proof at all) but one has to blame LF for not adjusting to an omniscient person being around. LF clearly knew that ("chaos is a ladder") and should have prepared to either leave winterfell asap or to rid himself of bran. But he decided to just ignore it which is absolutely stupid
Of the things LF knew that the Starks knew, nothing could bring him down. Sansa doesn't know the Lysa/Ned story. Arya knows the Tywin-LF connection, but LF doesn't know that. LF's biggest risk was Sansa/Arya, which is why the show spent all that time showing Sansa/Arya's deception of LF. (Which most people said was irrational from the characters, even though it was patently obvious that the characters were deceiving LF.) But that wouldn't have happened if they didn't have access to WeirwoodPedia. LF was scheming the whole season, it's just that he was out-schemed by people with way more knowledge.
Also I don't think LF knew Bran was some god-like figure. Which is more likely, that a cripple boy heard your catchphrase from somebody or that he's stream-sniping the entire universe?
Besides, his downfall is supposed to be symbolic. Ned fell when he went south but found that people valued power over honor. LF fell when he went north but found that people valued honor over power.