We just came back from our trip to southern Nevada - beginning of July 2004. We spent two nights in Mt. Charleston area (camped in the Kyle campground - very nice man who runs the camp). It was during the week and parking at the "false" trail head for Mt. Charleston- south loop was not a problem. There was only couple of cars. Also we met only two people and they were already going back from the summit on the south loop, so weekdays are definitely better if you like to feel more secluded.
But because we camped in the desert for the rest of the week we came back from Red Rock Canyon to camp here for the last night, it is definitely much cooler. That was on Saturday. We spent the day in Red Rock and came back to camp and put in at least one more hike - the Cathedral rock. The trail head to this one is couple feet away from the Charleston Peak - south loop. We decided to park at the "false" trail head again, because it was already 6pm and the Cathedral Rock picknic area closes at 8pm in summer. Also who wants to pay $5 for just been couple feet closer? Well the parking was full and there were cars parked in the right shoulder so we parked there too (I read in the Mt. Charleston-South loop trail page that they tolerate it and also, you are in the middle of woods.....!!!!). By the time we came back, before 8pm, there were not many cars left and only ours was in the shoulder with nice fat parking ticket for $50. So beware of this, maybe it is only on weekends, but they don't tolerate it anymore.
The gated picnic area is now only open on summer weekends at 10:30, too late to be of use to most Griffith/Charleston summitters.