I start caring about bye weeks with my #3 QB, #4 RB, and #5 WR. If my #2 QB has the same bye as my #1, then I'm not going to take a THIRD QB with the same bye, as well- it seems silly. Your 3rd QB is never going to see the lineup unless your top 2 QBs are down and out, anyway, so a lesser-rated QB3 with no bye week conflict is worth more than a higher-rated QB3 who's out the only week you'd consider starting him. This has come up in one league I'm in, where my QB1 is Brady, my QB2 is Palmer, and the best QB left on the board, in my opinion, is Campbell. I'm not taking a lesser player as a result of the conflict, I'm just grabbing value players at other positions (because there are ALWAYS value players at other positions) until such a time as a QB who doesn't have a week 8 bye starts presenting himself as good value. Ditto that with my RB4 or WR5- if two or three of the guys in front of him have the same bye, I'll look to avoid that week unless someone presents insane value (not likely late in the draft, since everyone past round 12-13 is just a differing degree of crapshoot).
If I have a stud TE1, I'll also take byes into consideration with my TE2 (since he's only playing if the TE1 is on bye), but if I have a mid-level TE1 (an Owen Daniels or a Chris Cooley, for instance), then I won't worry about byes with my TE2. With my PK and Defense I never even think about byes, because the junk on waivers is generally as good as any PK2 or DEF2 I might consider rostering.
I never worry about byes across positions. If my QB1, RB1, RB2, WR1, WR2, WR3, and TE1 are all out on the same week, then so be it. That week's pretty much a guaranteed loss, but I'll be the only guy in the league who doesn't have a single player on bye in any of the 7 other bye weeks, so I figure I'll make up at least one win somewhere down the line.