I understand the NBA and NHL do a version of this, and I wonder if the NFL has toyed with the idea at all. Essentially, rather than the last place team automatically drafting #1 and so forth, all the teams that failed to make the playoffs would be entered into a lottery to determine draft order.
The Pros: Discouraging the disgusting phenomenon of a team "mailing it in" upon failing to make the playoffs by removing the incentive to lose, making all the late-season games more meaningful. Allows perennially middling teams, like the Buffalo Bills, a chance to get a key player or two to elevate it to the next level.
The Cons: Some teams could get stuck at the bottom.
After last year's "Suck for Luck" embarrassment, and Goodell's willingness to tinker with the game, why not give this a try? Of course, I am biased because it would benefit the Bills now, but I do think it is wrong that in a competitive league there is any reward for losing.