If you ever see lots of 404 entries in your Apache or other webserver logs, then it is possible that malicious software has been used to try and attack the website - trying out a list of known URL paths and checking the HTTP response codes to try and identify any installed software such as content management systems or server administration tools, such as phpmyadmin.
Upon a successful hit, the software then proceeds to try and identify the version by looking at files such as README.txt, README.md or LICENSE.txt which might be present in the same folder. Upon identifying the version, if there are any known exploits for that software version, the malicious software then deploys the exploits and completes a successful attack of some kind.
I mention this simply to raise your awareness, perhaps it is also worth checking your webserver logs to see if a pattern like this has taken place. An IPS-enabled firewall or the Apache
mod_security add-on can help address issues like this.
However in your case, and more specifically to answer your question, for the entries to be in Webmaster Tools the links must have been indexed at some point, and I think this article by Susan Moskwa (Google Webmaster Trends Analyst) should help put your mind at ease.
To me it mostly sounds like you have lots of soft-404's because your website when it gives end-users a
404 File not Found error page, it's actually possibly returning an HTTP 200 (OK) response code instead of the corresponding HTTP 404 response code in the HTTP headers.
To be certain, it's worth double-checking: Go here and select the HTTP Headers option on the left, and paste in one of the URLs from your Webmasters Tools 404-list and see if the headers returned include
HTTP/1.1 404 Page Not Found. If not, perhaps you need to modify something in your website's page-not-found mechanism - for example in PHP to add the line
header('HTTP/1.1 404 Page Not Found'); to the top of the script before any HTML code is output.