It's not exactly a big secret that the Mets need, in some order, relief pitching, a lefty masher not named Wright or Hairston, and a backup/platoon catcher that isn't offensively hopeless. In an ideal world, said lefty masher could play second, first and corner outfield, allowing them to sit one of the lefties at those spots on a rotating basis, and not come at a huge cost, since the Wilpons aren't going to be looking to add a ton of salary. And, while we're at it, I'd like a unicorn that pisses beer and shits pizza.
Of these three priorities, I view adding a right handed batter as the most important, then catching. While relief pitching has been the most commonly lamented issue this team has, relief pitchers are notoriously inconsistent; I'd just as soon see if Josh Edgin or Jenrry Mejia or Pedro Beato can fix the 'pen and banish Miguel Batista and his putrid 6/5 K/BB ratio to the netherworld. For what it's worth, I'd also bet against Jon Rauch giving up 3 homers in 8 innings again anytime soon, and its worth noting that Frank Francisco has gotten significantly better as the season's gone on (before his injury). So I wouldn't go out of my way to pick up relief pitching.
One name that comes to mind is Josh WIllingham. Willingham is having a fine year on a Twins team that likely won't be a contender until he's long gone, or at least past his usefulness. He's posting a sterling 1.165 OPS against southpaws this year, and .921 overall (151 OPS+), making him more than worthy of an everyday spot in the lineup. His .298 BABIP is dead on his career average, so a sharp falloff isn't likely. Willingham is due $7 million each of the next two years, and the rebuilding Twins probably wouldn't mind getting out from under that contract, so the cost in players shouldn't be huge. The downside is that Willingham is limited to left field or DH duty at this point in his career, and if the Mets were to play Willingham and Duda at the corner OF spots, they're going to need a CF in the Peter Bourjos class just to avoid being completely terrible defensively, as WIllingham sports a -0.9 dWAR.
Reed Johnson would be a great pickup if only to ensure that he never faces Johan Santana again. Johnson plays all three outfield positions competently. I haven't discussed center field, but with Andres Torres constantly hurt and Kirk Nieuwenhuis' magic fairy dust wearing off, having a guy who can play center and hit lefties wouldn't hurt. Johnson has an .870 OPS against left handed pitching this year, not too far from his career mark of .834. It should be noted that his .381 BABIP against left handers is likely unsustainable but a dramatic falloff isn't too likely, given his .358 career. Johnson is a one-year rental, and the Cubs will be open to dealing anyone not named Anthony Rizzo or Starlin Castro, so I'd have to think that at most, a B-grade prospect would be enough.
Carlos Quentin's name has come up, as he: a. plays for a crappy team, b. is a right handed 1B/corner OF and c. has hit pretty well this year. But the bidding on Quentin will probably be high, he's got a track record of DL time that would make Nick Johnson say "damn!" and he's actually worse against lefties than righties. True, Quentin's career .803 OPS against southpaws would be an improvement over many of the ciphers that sit in the Mets' lineup, but the Mets need more than that for the return the Padres would likely demand.
Michael Cuddyer might actually be the beer-pissing, pizza-shitting unicorn I mentioned earlier. As recently as 2011, the 33 year old Cuddyer played 1B, 2B, and RF. Granted, he played second base poorly, but the Mets have already made the organizational decision to sacrifice defense for offense at second by virtue of putting Daniel Murphy there, so what's the big deal? Why not use Cuddyer as a regular right fielder, giving him some at bats at 1st and 2nd when Davis or Murphy require the inevitable off-day against a tough lefthander? The Rockies are terrible, and getting out from under the 2 1/2 years left on Cuddyer's 3 year, $31.5 million deal would be advisable. Cuddyer mashes lefties; he has a career .871 OPS against them, and was an awesome .993 last year. I don't normally pay a lot of attention to the inflated stats from Colorado, but Cuddyer might be the rare Rockie that improves after going elsewhere; he's at .891 this year, despite a freakishly low .226 BABIP against lefties. However, with a market low on sluggers, the Rockies might be able to demand a significant return for Cuddyer even without picking up some of his contract.
Among catchers, unfortunately, the pickings are slim. Miguel Olivo was mentioned elsewhere, so I'll redirect you to this post for further detail on why he makes some sense. Olivo should have a significant second-half bounceback and should add some punch to the lineup in a place where it's sorely lacking. He's a short term commitment; he has a $3 million team option for next year that I'd be surprised to see anyone pick up unless he has a Mike Piazza-like second half. The only other potential option that makes any sense is Ryan Doumit. Doumit is a switch hitter who's better against righties in his career (.803 OPS vs. .715), but he's at least better against lefties than Josh Thole or Mike Nickeas. He can also pitch in at 1B or RF if need be. Like Quentin, Doumit is no stranger to the disabled list, but in a part-time role, he should be fine. He's a free agent after this year, and the Twins should be willing to take a B-grade prospect for him.
Finally, let me address the elephant in the room: the (oft) injured Jason Bay. I'm not keeping a candle in the window for Bay. Apart from the fact that Bay can't stay healthy, his career arc is pretty clearly suggestive of a steep decline. That $16 million salary would sure go a long way toward getting some badly needed help. Alas. To be fair to Bay, it's possible that he may have some value; he raked lefties to the tune of a .918 OPS, though that was helped mightily by a .378 BABIP which was over 50 points above his career BABIP vs. lefties. And remember, that career number includes the years when Bay was actually good. Still, improvement is inevitable; if last year's .378 was unsustainably high, so is his .154 this year unsustainably low. Unfortunately, unless Sandy Alderson can convince the Wilpons to loosen the purse strings a bit, or come up with a creative option, it may well be Bay they're relying upon.