This line should have been a pretty good indication of what was/is wrong:
[Mon Oct 7 13:54:57 2002] [error] server reached MaxClients setting, consider raising the MaxClients setting
Basically you have too many concurrent users hitting Apache at any given time. You should either raise the default MaxClients setting from 150 - 300 (?) or consider balancing out the machines load over 2 boxes.
Just some more information. The default setting for MaxClients (and the max value unless you recompile for apache 1.3 on most UNIX OSs) is 256. If you have specified a value less than that, you'll probably want to remove it (to use the default) or raise it to 256. If it's already set at 256, you may need to recompile to raise it. There is probably a thread or two on here if you search that will help you do that.
Lowering the KeepAliveTimeout might help.
This is more than likely just a symptom of a larger problem.
You should only get that warning message when starting apache. Are you running it in inetd mode? Anyway, that's just a warning, you can probaly ignore it. To get rid of it, remove the NameVirtualHost directive for 66.250.110.###:80.
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