If you actually mean "weakness" when you said "problems", the answer is yes. By modifying Bitcoin protocol, you might able to solve current weakness of the protocol, although it's likely the modification actually perform trade-off rather than improvement.


If it's not critical vulnerability (which means the problem won't get CVE code after it's published), you could just publish your report/analysis report somewhere (e.g. in your blog or this forum) and share link to few Bitcoin community.