While it is very common, I find this sentence a bit ugly, and slightly incorrect. The noun adjective "viewer"—which I presume it must be—is ugly here, probably because it suggests that the entire noun phrase is a common term ("viewer discretion"), which I believe it wasn't until this formula was invented.
We could rephrase it as "we advise the viewer to use his discretion". We need "his" because the use of a noun adjective suggests possession. But "his / her / the King's discretion" is mostly said of people with some discretionary power, like a judge who has the right to make a decision based on his own judgement as opposed to on some external rule or power. Now, that is not what it is supposed to mean here; the phrase is somewhat misleading on that account.
What might have been intended was that the viewer should "use his own discretion" to decide whether he wanted to keep watching, which means his own ability to discern what the right course of action is in a given situation. But then we'd get "we advise the viewer to make a sensible decision": that is nearly a tautology. If this is the advice we get, then it is an out-of-control euphemism that hardly means anything. Moreover, the formula should then be "viewer's own discretion advised".
Alternatively, what is intended might be that the viewer should "use discretion": this means that he should be careful when considering his options, presumably because he will regret it if he doesn't give this decision the attention it deserves. This is the most reasonable explanation of the formula—but then it should have said "viewer is advised discretion": otherwise the viewer would be taken as the possessor of the discretion, which would take us back to "his discretion" as above. Moreover, "caution" would have been better then, because "discretion" usually means that you need to be careful in your behaviour with regard to its effect on others. In short, "viewer discretion", while not absurd or entirely impossible, is slightly off.
Using the passive voice in a notice like this—it may be a bit stiff, but it looks quite all right to me this way. It is clear that whoever is responsible for broadcasting the programme is advising the viewer.
In your definition no. 2, personnel is used as short for personnel department, i.e. the department of a company responsible for hiring and firing personnel. It is just like research standing for research department, etc.
Better take those papers to Research. Or, wait, I think the guys at Personnel should have a look at it first, since it concerns hiring new research personnel.
I consider the word personnel to be singular. The plural personnels is not used, because this word is a collective noun, i.e. a singular noun that can be treated as plural and gets a plural verb, just like police, family, etc. Whether to use a singular or plural verb depends on whether you are thinking of the group of people that make up the personnel (plural), or rather the concept or unit of personnel (singular, less frequent).
The personnel have been complaining about working late.
Our well trained personnel is our greatest asset. (Plural might be possible too, but probably less common in this sense.)
I think Personnel is not going to be happy about moving to a new building. (The Personnel Department; plural would probably work as well? Not sure.)
Note that plural verbs with collective nouns are more frequent in England than in America.
[ Some people would call collective nouns plural, but I'm not a big fan of that. I consider plural primarily an inflectional quality, its syntactic ramifications being secondary. That is how plurals are analysed in other languages as well. Just as we only call committees plural, never committee, not even in sentences like the committee have come to a decision. But I can understand if some people might disagree. Each model has its merits. ]
Best Answer
I believe the distinction here is between choices, as you pointed out. The choices appear in the next phrase: "[...] to repair or replace defective equipment [...]".