I have an instance of Solr, hosted with Tomcat that recently started creating minidump files. There are no errors in any of logs, and Solr continues to work with out a hitch.
Are you using Java 7? In that case revert to Java 5 or 6. Lucene/Solr and Java 7 don't go well together and it could be this creates the dump files. Otherwise if everything is working, just disable the dumping of files.