It's pretty easy to not get into trouble with wet spots and such at the Bonneville salt flats -- just pay attention to the map that is available, make sure you follow the cones and instructions, and don't get to taken with exploring once you think you've got it all figured out.
As for the pits - well, without a pit pass you aren't allowed to drive into the area. You're welcome to walk about or ride your bicycle, but to drive a vehicle you'll need that pass - which you get by being registered on a crew or team. Speed limit in the pits is 5 mph - because most of the race vehicles that will be moving are being pushed or pulled and don't have brakes or other such niceties, as well as (usually) compromised vision from the driver seat. Be extra careful and give the racer every consideration.
As for getting too close (for instance) - common sense rules. There are no rules to prevent you from getting close up to the pit - - other than if the crew asks you to back off you should back off. If there's something going on that's causing high stress levels you might be greeted with a bit of a raised voice, so be aware. Other than that -- it's not unknown at all for a spectator to wander a bit close to a pit and, upon being seen by someone working in the pit, being told something like "Hey. Would you mind coming here and grabbing this wrench and holding while I tighten this?" There are not many secrets in land sped racing, so not many times will you be chased away for the possibility of stealing a super-secret idea.
We look forward to seeing you on the salt.