How much presence does law enforcement have in Black Rock City?

Yes. I remember hearing that there are 20-50 government agencies involved. The ones I can remember with clear visibility are:
BLM Rangers
Pershing County Sheriff's Dept.
Washoe County Sheriff's Dept.
These guys drive around in big shiny trucks and are generally concerned with violence, drunk driving, damage to the land (especially BLM), lewd behavior (generally only involving minors, though they once made Jiffy Lube move their sign), and drugs.

The ones that are probably there:
FBI
DEA
ATF
Nevada State Troopers
Nevada Health Department (they sometimes shut down bars and places serving food)

The ones that my conspiracy sense says are there:
CIA
NSA
Secret Service
The theory is that these guys, along with the FBA and ATF, would be interested in people who know so much about explosives. There are also just a lot of libertarian gun-toting types at Burning Man, and these agencies like to keep up with them.

There is a legend of a naked drug enforcement officer, and this legend is true. She seems just like a naked burner because she is one. She's been coming for years and apparently loves the event, just like most of the law enforcement people. (Many of the volunteer to work the event and bring their families out with them.) The only difference is that, after hanging out with you for an hour and talking about all kinds of stuff and smoking some pot or whatever, her friends come in and arrest you.

The agencies all have their own camp outside the gates where the monitor all the radio frequencies and keep track of everything that's going on in the city. In recent years they've also been putting cameras in some of the cars.

All of that said, here are some tips to avoid going to jail, besides the obvious advice of "don't do anything illegal," which is my official position.

1) Don't smoke pot in view of the road.
This is the single most risky thing you can do as far as law enforcement is concerned. Unlike many other illegal substances, pot smells strongly of pot and leaves a smoke trail pointing right to the pot smoker. If you must smoke pot for medical reasons do it out of sight in a place that is legally your domicile. (Get a lawyer to explain it.)

2) Don't discuss drugs with anyone you don't know.
If someone wanders into your camp and asks for drugs they are either a cop or a total loser. Either way I always politely say "fuck you narc, go back to narc school and learn how to not be such a lame ass narc."

3) Don't drink and drive.
This is just as illegal there, and much more stupid and dangerous.

4) Don't speed on the way in.
Follow the posted speed limits EXACTLY. Burning Man is a speeding ticket windfall for all of the little towns on the way out there. If you want to support the locals it's way cheaper to buy and indian taco.

5) Don't talk.
If the police detain you and you have some reason to be afraid of them say nothing but your name. Tell them you want a lawyer present for any search or questioning. Ask a friend (or anyone) to go find a Black Rock Ranger and request that they help you locate a lawyer. They have a legal team that really wants you to not get arrested. For god's sake don't argue with the police or say "but this is burning man!"