When I was in my early 20s, I always thought once the Redskins were mathematically out of the playoffs, they should lose out to ensure a better draft pick. I now know that logic is beyond imbecilic.
First, we're in a phase where we are evaluating talent. The Redskins have a lot of holes right now, so we should want to see our players and team do well. The emergence of Rob Jackson, (potentially) Kevin Barnes, Anthony Bryant, Perry Riley...this is good news. These are guys that have shown they can take what they've learned in practice and execute. If they stink it up, drafting three slots higher doesn't mean we can fit three holes with that earlier pick.
Second, winning is important for the team in many ways. Players are hammered a game plan all summer and every day of the week. The players need to know the coaches are winners, too. Beating Jacksonville and the Giants does have a positive effect moving into the off-season and OTAs.
Third, and most important, if the Redskins have good talent evaluators, then a few spots in either direction shouldn't make a difference. Mel Kiper and twelve million idiot bloggers like me will have their player mock draft rankings, but as we see each and every year, the coaches rankings are much different. Shanahan hit a homerun with Trent Williams (while 99% of us called for Russell Okung - who's only played 9 games this year).
Take a look at this chart. It lists the round and draft pick number for each of this year's top 5 players in every category. An early teen pick will do just fine for the Redskins. Trading back is not a common move, so I'd rather take the extra wins and a better evaluation of our current roster any day of the year.
Note: If the Redskins ever, ever draft a running back in the first round, especially high, I might have to kick Ken in the sack. Beanie Wells, Knowshon Moreno, Reggie Bush, CJ Spiller (though he's getting misused horribly), it's a waste of a pick - especially given the life of a RB.