While reading about the 77/357 on various websites, I've seen some people claiming two things for both the 77/44 and the 77/357.
Check the trigger if at all possible. There are a lot of claims of trigger problems (too heavy, stage-y, spongey, you name it). As far as how true that really is, I honestly don't know. My 77/357's trigger is fantastic as far as I'm concerned, but what is fantastic to me might be absolutely horrid to another.
The next one claim is a tough one to check before you buy, and that is that some of them just aren't accurate. Again, as with the other claim, I don't know whether it's the shooter or the weapon and I'm not about to open that can of worms, so all I'll say is that my new in box 2011 produced 77/357 I got recently is utterly accurate, with both bulk and high quality/pressure ammo as far as I'm concerned. To be completely forthright though, I only use iron sights, so clover leaf groupings at 100yds every time is not a criteria for me.
Outside of that, I've actually not come across any magazine problems or complaints for the 77/44, unlike the 77/357, so there's a plus!
And if I may be so bold, go for the stainless G-1 Vista camo pattern one!!
Barring that get the stainless and synthetic stock. Three reasons for doing so; first being the ease of maintenance, second being that it looks better and third being that the walnut stock can be bought separately and put on while retaining the beauty and ease of stainless steel.