The short answer is no, there does not need to be video tapes or pictures to arrest someone.
In order for an arrest warrant to be issued, there must be "probable cause." This basically means that the police officer must show a reasonable belief that your nephew has committed a crime. This is a lower standard than most people think. The police in this case have a witness. That is most likely sufficient probable cause to arrest your nephew.
However, that being said, "probable cause" is the standard used when arresting a person, not when convicting a person. The standard for conviction is "beyond a reasonable doubt." This is a much higher standard.
Often, there is sufficient evidence to show probable cause to arrest someone, but insufficient evidence to convict the same person. This may be the case with your nephew. You should consult a criminal defense attorney immediately.
In Florida the answer is no. Your nephew may have an entrapment defense if he can prove this reverse sting operation used a confidential informant who called your nephew at all hours and basically harranged him into buying the pills. Usually these cases are set up through a friend of your nephew who knows he may be a potential target. Also the CI is usually charged and trying to help himself. Sometimes a CI introduces and a law enforcement officer completes the transaction in which case the chances are more likely that they will be believed and also appear at any trial. CIs tend to be less reliable witnesses and can disappear so that if there are there is no audio or video his chances of making a deal or getting charges dismissed are better. However in the mean time your nephew may think about doing some drug treatment. Definately he should get an attorney
The evidence in these cases varies and can include video and photo surveillance or testimony from the alleged buyer. However, in most cases the evidence comes form the testimony of the officer who surveilled the alleged transaction or participated in it directly.
The law doesn't require any particular form of evidence: the question (at a trial) is whether there is enough evidence to prove the charge beyond a reasonable doubt.
Although their doesn't have to be a video tape, the police have a standard practice which they follow when they use informants. The informant is searched before and after the "buy", and there is an officer or officers watching him, at least until the time he goes into a residence. The police keep a log recording this information.
Your nephew's lawyer should obtain this information during the course of defending him.