1) Don't make your epic someone else's epic as well; routes converge, so you want to be fast, especially near top. If you don't belong on this route, wait a year and do it in style.
2) Don't overextend; this is not a climb for borderline 5.10 leaders
3) Don't underestimate the weather; it is almost always cold, and it can snow harder here in the summer than it does in most places in the winter.
4) Practice on comparable climbing; this is not the place to figure out how to haul a pack, to work out communication with a partner you can't see or hear, or to find out how slow you are, etc. Chasm View Wall has some high quality climbs of comparable difficulty, but much less commitment. Think about going up to the Mills Glacier bivy and doing Chasm View before hand - it also gets into shape (i.e., is dry) much earlier in the season
5) This is at times a crowded wall; try to avoid weekends; be considerate of others (don't drag ropes across loose ledges, knock off rocks, bellow at your belay partner, etc.) Share the alpine experience...
6) If you can, talk to the climbing rangers at the trailhead. We found them to be well-informed and very helpful. On the other hand, the "back-country" rangers who you can call on the phone were not very knowledgeable about technical climbing conditions, etc. The folks at Neptune's (Boulder) often have current knowledge of conditions, etc.