. . but not so much problem. Education efforts have been intense and ongoing for many years and in many languages. Enforcement has always been intense and everyone knows about it.
It helps that California is a major agricultural state and has such a wide climate range. If there's a market for anything it'll soon be grown here and certified, and the import markets are very well organized and regulated for stuff that isn't grown here.
"Rodent", though, isn't widely available except for rabbit, and to make a propper haggis you'd have to buy your own sheep because sheep lungs aren't legal in trade here.
We do have a continuing problem with Asians trying to stock local streams with live snakeheads, definitely a problem fish and highly illegal to posess live, but legal and widely available "previously frozen" in local Asian markets.
The big dispute has been about how long rice cakes can safely be kept at a cool room temperature (they're ruined by refrigeration). The state backed off on enforcement and is currently studying just how long they can allow and still assure safety.
It's very difficult for a traditional Chinese restaurant to get an "A" window sign from the county inspectors because of incompatibilities between food regulations and traditional methods. It has been done, but most Chinese restaurants settle for a "B" or "C" (below "C" there are numerical ratings but you will never see one posted because any establishment below "C" is closed until corrected).
In most parts of Los Angeles County a lot of people will only eat at an "A" restaurant and certainly not at a "C", but in traditional Asian areas the "C" is hard enough to get it's considered good enough.