It runs in 640x480, so as you can imagine every bit of anti-aliasing helps.
Efforts were made a few years ago to get Grim Fandango running in your native resolution and simply stretching the background imagery up, which makes the jaggies much less pronounced. However, the attempts were abandoned as although the models could be scaled up to higher resolutions the backgrounds stayed at their original 640x480 size in the corner, with the models placed over a black void.
There is another project called GRIME which is a sub-project of ScummVM, which I believe will eventually
become the only way of running Grim Fandango on modern machines, and may have ways to use higher resolutions. However this is barely usable right now and didn't work past the first chapter of the game last time I checked. Feel free to go Google that up, though.
As it is though, you unfortunately have to live with stretched 640x480. I personally think horizontal stretching looks really bad as it obviously messes the proportions up, and I use black bars (even in newer games that hilariously don't support widescreen such as Battlefield 2142).
It's entirely down to your taste, though; I know many people who don't mind horizontal stretching, even on television, and think it's a worthwhile compromise for filling the whole monitor.
If my camera wasn't broken I'd get it running on my 24-inch monitor and take a photo so you can see roughly how it looks.