Three shots (12 & 16 ga), 4 or 5 (.410) faster than a single shot break action gun.
Often not quite as well balanced and handling as a good double barrel or single shot, but not something that cannot be overcome.
Not as efficient as a pump, or semi.
James K gives a pretty good summary, but I would disagree with this, slightly..
One was the 1968 Federal law which required all guns have serial numbers.
The law does not require all guns to have serial numbers. It requires all guns made after 68 to have serial numbers. Guns made before the law took effect are not required to have serial numbers, UNLESS the maker put on it, originally, and if they did, then it is required, and required to be "readable", meaning not defaced or removed. If the gun HAD a serial number at one time, and that number has been removed, the gun is now illegal to own. If it NEVER had a serial number, you don't HAVE to put one on it, and it is legal to own.
I don't think the added expense of stamping a few numbers into a receiver to be what killed the popularity of the bolt action shotgun. I think it was more the other factors James K mentions, along with the elimination of direct to the customer mail order sales.