How to handle newly discovered problems in second and third round reviews
(1) The comments of other reviewers should not bother you; often reviewers will be from mutually exclusive fields, so as to provide better representation. You should stand by your professional opinion irrespective of the others.

(2) I firmly believe that you should spend a lot of time on first and second review. If you are finding new and significant errors beyond these rounds, it means you didn't do your job rigorously before.



EDIT: Several comments highlight the valid point that sometimes revisions are required just to make the paper readable. My position on this is that if more than 2 'readability-reviews' are required, the authors are either unable to use the language adequately (and should be directed to a suitable resource- a reviewer is meant to check technical content, not be a style coach), or are unwilling to make these suggestions; in which case there is no point asking once again.



Comments/questions regarding your previous objections are ok, but entirely new objections in third or subsequent rounds leave a bitter taste and lead to a lot if time being wasted.