I can't seem to find any documentation on this. Is there a limit to the number of characters that can be used in a filename and/or is there a restriction on what characters can be used in a file name saved by an iPhone app? Thanks.
The underlying filesystem is HFS+ which limits filenames to 255 UTF-16 characters. There may be additional restrictions on the filenames but I'm not aware of any.
According to this site, the only forbidden character on HFS+ volumes (which as Michael Greene stated is the underlying filesystem on the iPhone) is the colon character. You may also have some trouble using the '/' character since OS X tends to treat those as directory separators, too.
I don't know if the colon (:), a folder separator from HFS days still applies but it is better to avoid such characters.