I don't really see a problem with mentioning one singular activity (of the criminal sort). Conversely, several "criminal activities" are not unusual, either.

I agree with Amy, "act" or "action" would both be better here, and "a criminal activity" does sound a little strange.

I don't dispute that criminal activities are possible; the countable noun just doesn't seem appropriate in this context. The speaker doesn't refer to criminal activities like theft, gang activity or drug use, he refers to one specific act, namely a shooting.

FWIW, your source is not the only one to use "criminal activity" as something countable. There seem to be lots of others:

http://www.htpsecurity.com/services.htm
The PPO/s primary task will be to detect, deter and prevent a criminal activity from occurring.

http://intercominnyc.com/cctv.general.php
These type of cameras makes people aware and can sometimes prevent a criminal activity.

http://www.vidalinsuranceagency.com/PrivacyPo...
To an insurance institution, agent, or credit reporting agency in order to detect or prevent a criminal activity, fraud or misrepresentation in connection with an insurance transaction;

I agree with Ami-MiMi's position.

I really don't see what the problem is:

http://www.macmillandictionary.com/thesaurus-...
surveillance noun
the process of carefully watching a person or place that may be involved in a criminal activity

https://www.igolder.com/glossary/criminal-act...
What constitutes a "Criminal Activity"?

http://www.ncbi.nlm.nih.gov/pubmed/16730253
Is scientific publishing a criminal activity?

http://www.lawteacher.net/criminology/essays/...
Identify a Criminal Activity
Identify a Criminal Activity: male aggression against women

I accept some of the examples in #6 (assuming they do not refer to an isolated event), but not #0, They can sue the state for negligence for failing to prevent a criminal activity from occurring. 

Maybe it's the focus on specific acts vs. a category of behavior.

Smuggling (in general) is a criminal activity, but a smuggler caught red handed is not arrested for a criminal activity (although possibly for engaging in a criminal activity, i.e., a criminal enterprise or pattern of behavior).

I agree that using 'activity' to mean a specific act or incident, as opposed to an ongoing pattern or category of behavior, sounds wrong, even if it reflects language actually used in laws somewhere. Unfortunately, laws are written by legislators, and they don't always pay attention to writing good English.

Wonder if Garner has anything to say about this point in his book on legal usage (which I don't have).