Ron is absolutely correct. In most states, if an officer is performing their public duties, in a public place, it is perfectly legal to video record the incident.
While there have been some widely publicized incidents where cops have overstepped their authority regarding someone videotaping them, there can be legitimate legal issues regarding HOW the person making the recording goes about it. For example, even if they are on duty, it would be illegal in some states (don’t know about FL) to follow a cop around and record their every move. That could be considered stalking. Likewise, it is not legal for a “citizen journalist” to interfere with an officer’s duties…like refusing to move a safe distance away (he/she doesn’t know you or what your intentions are so is forced to divide attention between the subject they are dealing with and you – compromising their safety), yelling for bystanders to intervene because “he didn’t do nothing!” (that’s called inciting a riot), or telling the person being detained/arrest to not comply because “you don’t have to do any $hit they tellin’ you to do!” (obstructing a public servant). So, while it is legal to record the cops (and, remember, in many jurisdictions the cops are recording the incident, too!), don’t get jammed up by taking it too far.

