Historically, the right side of the Eagles' offensive line has been the hammer. When (or rather, if) they ran the ball, more often than not, they ran it behind Jon Runyan and Shawn Andrews, and before Andrews, Jermane Mayberry. The left side's primary job was to keep Donovan McNabb off his back.
The landscape of the Eagles' OL has since changed. The hammer is now the left side, as Jason Peters and Todd Herremans both excel in the run game, and when the Eagles absolutely need to run the ball, they're running left. Look no further than the 4 minute, bleed-the-clock drive against the Cowboys in which Peters and Herremans physically dominated the Cowboys' D line and effectively sealed the win:
Almost coincidentally (and I say "coincidentally" because the Eagles certainly didn't plan for this), the Eagles now have a left-handed QB in Michael Vick. However, in contrast to the Eagles teams of the aughts, the OL didn't do a good job protecting the QB's blind side last season. Both Winston Justice and Max Jean-Gilles are below average NFL starters, and while Mike McGlynn showed promise at times this season as the starting center, he also struggled at times. That's not the personnel you want to have protecting the blind side of your star player.
According to Jason La Canfora, the Dallas Cowboys are not expected to use the franchise tag on any of their players, which could be an enormous mistake. The Cowboys' best and most valuable offensive lineman by far, LT Doug Free, is set to become a free agent. Free isn't going to drive many NFL defensive linemen off the ball and open up holes in the run game, but he is very athletic, has extremely quick feet for a guy his size (6'6, 320), and excels in pass protection. Here's an example of Free's athleticism. Watch how quickly he gets downfield from his RT position and rides Sheldon Brown for literally 25 yards against the Eagles in the 2009 regular season finale:
Although Free played LT this past season, he has experience playing the right side, and would be an absolutely perfect fit on the Eagles OL protecting Michael Vick's blindside, now that the responsibilities of the left and right sides of the line are sort of flipped. The Eagles could then look to shed Justice's contract (salary of $2.7 million in 2011) and deal him for whatever they can get (probably little more than a late-round pick).
The more fun aspect of signing Free though would be the devastating effect it would have on the Cowboys' offense. It's no secret that, on the whole, the Cowboys' OL was awful in 2010, as their poor play contributed to their surprise 6-10 season. RT Marc Colombo was dinged up early and had a wretched season. He may be done in Dallas. Ditto that for Leonard Davis, who was benched at one point during 2010. LG Kyle Kosier battled injuries for most of 2010 and also had a down year. C Andre Gurode made the Pro Bowl again, but mainly because center is an extraordinarily weak position across the entire NFC. Hell, Shaun O'Hara of the Giants made the Pro Bowl at center despite missing half the season and playing poorly when he was actually able to go. And oh by the way, Gurode will be 32 in March, and the other 3 above-mentioned Cowboys offensive linemen will be 33 by the end of the 2011 season. As it is, the Cowboys will already have to work a minor miracle to fix their OL as it currently stands. Losing their best and only young offensive lineman (Free just turned 27 in January) would be an absolute disaster.
Jerry Jones probably should tag Free, and he still has some time to change his mind, but even if he doesn't, I'd have to imagine that re-signing Free will be a top priority for Jones. There's also a possibility that the new CBA will force Free to be a restricted free agent, which will basically keep him in Dallas. Whatever the case, Jerry Jones is rolling the dice bigtime by not tagging him... right now. If Free should become... you know... free, he'd be my #2 free agent target behind Nnamdi Asomugha.
Disclaimer - I swear I'm normally not an "Oh my God, we have to sign this player, and that player, and that player" type of guy. But there are just so many intriguing names out there this offseason that fit the Eagles' needs so perfectly, and they have the money to spend. It'll be a major disappointment if the new CBA isn't done soon and the Eagles don't have the chance to add serious talent to their roster.