As Illustrator is generally vector based, resolution is not really an issue. There are two exceptions I know of:
1: Placed raster artwork
If you import photos or other raster images into Illustrator, then 300dpi is good enough for magazines. If you scale your image up or down, you will need to adjust this resolution accordingly.
2: Path Output Resolution
The default value of 800dpi is fine for practically all purposes, but sometimes you might import artwork from another program, and it might be a lower value. When printed, this could result in curves that are made up of noticable line segments. It's not something that happens very often, so you can probably ignore it, but it's easily rectified anyway.