Hi John,
Sorry but there is no way to avoid logging some types of errors. You can disable logging errors but that would stop logging all errors.
What I do if I get lots of errors from the same ip address, particularly if they are from RIPE network or Asia Pacific network APNIC, I block them at the firewall to prevent them from causing so much noise. You can also block them from Administration > Advanced Tools > Banned IP Addresses.
Usually I'll search for the ip from the member list first to make sure it is not from a registered user. If the traffic was coming from the ip of a known user I would contact that user.
It is an unfortunate truth that for most sites the bot traffic is much more than the traffic of actual users. I've got similar noise in my logs from bots that constantly generate viewstate errors. They do this trying to exploit an asp.net vulnerability that has long since been fixed but they are hoping to find unpatched machines.
If you configure for database logging, then the log page has links fo the ip addresses that opens as a popup window and shows the whois information about the ip address.
By using the database I can also query to find the ip addresses that have the most errors, I use the built in query tool and a saved query:
SELECT IpAddress, Count(*)
FROM mp_systemlog
GROUP BY IpAddress
ORDER BY Count(*) DESC
If I see hundreds of errors from the same ip in a short period since the last time I lcleared the log, I often ban or block those ips from the firewall. However there are so many that my threshold of what I ban has gone up over time.
Best,
Joe