Is it a crime or otherwise problematic to use the symbol for registered trademarks in the U.S. if there is, in fact, no registered trademark present? And, if so, what is the penalty?
Symbol in question: ®
Summary from comments. (Hat tip @jqning)
[It] is not only improper it is UNLAWFUL and may result in serious repercussions...
Such a misuse may constitute false advertising... (“It is no doubt true” that affixing the ‘Trade Mark Registered U.S. Patent Office” notice on goods that are not protected by a federally registered trademark creates “a prima facie case of fraud against the public… .”).
Such use is also a form of “unclean hands” that can bar the user’s registration of the mark.
Such a use may also bar the maintenance of an infringement case.
And the fraudulent use of the trademark registration symbol DOES provide other marketplace participants with standing to oppose the user’s registration of the mark.
Well, you are lying. The problem isn't so much the symbol, but the claim that you have a registered trademark. And the question is whether your lie cost someone money, and whether that someone finds out and sues you.
Worst case, some company planned to release a new product under a new name, which they wanted to trademark, but they spotted your claim of a registered trademark for the same name, and changed the name, having to change documentation, product manuals, advertisement materials and so on. And then they find out that you don't actually have a trademark and it cost them a lot of money.
Nobody could say whether they would win in court, but if they take you to court, you can bet it will cost you a lot of money.