Well many SEP's will recomment that a C Class IP is always good for SEO, does that answer your question.
Yes it does matter if you are serious about your search engine marketing campaign. With shared hosting you can be on the same IP as a porn, gambling, or 35 doorway spam pages which can hurt your efforts. You will also be sharing the same bandwidth with those pages, thus your load time will be slower then if you were on a dedicated server. With a dedicated server you have control over what sites on are your IP, and the load time will be much faster. Load time is also important because being faster allows the bots to crawl more pages in a shorter amount of time. Search engines will not crawl your entire website on each visit, they only crawl so many pages in a certain amount of time as to not crash your website. With a dedicated you can serve up those pages quick. Some people will disagree and say it does not matter, but look at some competitive markets and I bet a majority of the sites are on a dedicated server for the reason's listed above.
Are there any issues, with respect to one's current search engine rankings, in changing from a shared hosting plan over to a dedicated IP address plan?