The definite article is not used in this expression.
When we assign an entity membership in a class we use the indefinite article, regardless of how ‘determinate’ the entity is, because it is not the only member of the class.
For instance, we ordinarily say “I own a ’57 Chevy”—that is, “The car I own belongs to the class ’57 Chevy”. You own only one car, it is entirely determinate, you introduce it into the conversation with the definite article; but it is just one of many ’57 Chevys. You would only say “I own the ’57 Chevy” if you and your hearers were looking at a group of cars and you were identifying your car as the only ’57 Chevy in the group.
Likewise, when you speak of a particular individual known to your hearer, you use a definite determiner in identifying or naming her—my wife—but the indefinite article in assigning her to a class: “My wife is a graduate student in mediaeval English lit.”
In the same way, when you say “What a car!”, you are not identifying the car but asserting its membership in the class of “cars to which attention should be drawn”.
We never say "What the X," because that utterance is not intended to identify which X you are talking about. It does not enjoin the hearer to "Look at that X", it observes that that X is an X of a certain class: it is an X which excites your admiration and deserves your hearer's attention.
There is nothing wrong with saying "the police." Here is just two articles from the New York Times, a newspaper that seems to prefer "the police":
Bikers Jailed After Waco Shootout Deride High Bonds and Slow Justice
WACO, Tex. — Matthew A. Clendennen, one of the nearly 180 bikers who were jailed after the deadly shootout here last month among rival biker gangs and the police, said he had one weapon on him during the melee — a pocketknife with a two-inch blade that was a Christmas gift from his parents that he uses as a screwdriver and box cutter at work.
...
They say the police used a “fill- in-the-blank” criminal complaint to charge all 177 suspects, that they arrested several unarmed men and women who were “recreational motorcyclists”
New York Police Detective Shoots Gunman Who Wounded Man
A New York police detective in plainclothes shot a 26-year-old man who had shot another man in East Harlem at about 8 p.m. on Tuesday, the authorities said.
The police said the unidentified gunman wounded a 21-year-old man on First Avenue near 101st Street. Two detectives driving in the area after a court appearance heard the shots and got out of their car, the police said.
Officials said the gunman was chasing the wounded man on First Avenue when he encountered the detectives. The police said the detectives identified themselves and ordered the man to drop his weapon, but he pointed it at them instead, prompting one detective to fire two shots.
Notice also "the authorities." The article also has "officials." So the NYT's use of the definite article with such terms is varied. If you check other articles in other newspapers or news sources you will routinely see "authorities" and "officials" along with "police" as having said something. (The) police is considered plural, so it fits right in there with the two plural words. In fact, sometimes (the) "authorities" are (the) "police."
There is little difference in meaning in this context whether one makes a definite reference (using the) or an indefinite reference (not using the). As far as journalism goes, it is a stylistic choice.
The article Police or the police? that Collin links to is pretty good. But it doesn't really say anything surprising.
Writers often use the zero-article with plural nouns when they want to make an indefinite reference. This indefinite reference can include being indefinite as to the number of, say, units involved, whether police or bullets or ants.
Bullets were flying everywhere.
is indefinite. We don't know how many and the author doesn't really care to tells us.
Ants were crawling all over the place.
Same thing.
Police were running everywhere. Police were crawling all over the place.
However, if "the" is used, it can refer to "the police department."
Quick! Call the police!
refers to calling the police department, or the police force. This is the same as when we say
Quick! Call the fire department!
But sometimes it is pretty hard to distinguish. If you are at the scene of a crime or accident and two police officers pull up in a police car, and you say the police are here, it's hard to believe that you are not referring to the two officers at the scene--at least as representating "the police department." Which is fine. We say the same when the firetruck pulls up with 5 firefighters: the fire department is here.
Other newspapers seem to be going away from using even the standard "call the police":
Manhunt focuses on prison area; Philly tip discredited (USA Today)
Meanwhile, Philadelphia police told USA TODAY that two men picked up by a taxi driver and taken to a train station before dawn Thursday were not the fugitives.
Police said the driver called police early Thursday to say he picked up two men who matched the duo's description before dawn Thursday. He said he took them to a train station and then took another fare to the airport before calling police with his concerns.
Police then sought surveillance footage at 30th Street Station and anywhere else that might be helpful. Officer Leeloni Palmiero said a review of footage revealed that the men were not Matt and Sweat.
I'm just highlighting the phrase call police because USA Today seems to prefer this over the normal, everyday phrase call the police. For many, this use of police without the the will seem strange (see Ngram below). And that is not all: analysis of Police or the police? falls apart. Because we don't call an "indeterminate number of police officers" when we "call (the) police," we call "the police department." And I won't be yelling "call police" any time soon. (And hopefully not "call the police" either.)
The conclusion, therefore, is that this is more of a style issue than a purely grammatical issue.
Best Answer
In both of the bolded cases, the noun does not refer to particular cases of the things mentioned, but to the classes of those objects in general. This is the OED's second sense of "the":
This usage is commonly seen with musical instruments, where the whole class of instruments is referred to.
Could mean that Bill is playing a particular clarinet right now, but more commonly will mean that Bill has the ability to play the class of instruments generally known as "clarinet".
This definitely means that Bill is in the act of playing a singular clarinet. (Not a particular clarinet that has otherwise been identified, but any given one.)
In this case, a particular clarinet is being referred to (and its identity has been previously established in context, as one of the five instruments). You could think of the word "clarinet" as having a different meaning in this sentence than in the first: here meaning an instrument of the class, and in the first sentence meaning the class itself.
To use "a beach" in this case would not be incorrect, but I think would be less common in a context like this; the different sense would be the same as the difference between my first two clarinet examples. In this case, the listener (or at least this native AmE listener) would get a vague sense that the speaker is being unnecessarily specific: the context is in broad general terms about "most vacations" "in years gone by", so it makes sense to refer to "the beach" in the sense of "the class of objects known as the beach". "A beach" would almost give the sense that all those people on all those vacations had been going to a particular beach (but from context it would be clear that that was not the case, so not really an error).
On the other hand, I think one would never use "a family" in this case. I think the reason is that everyone has one family (more or less), so it would seem strange to make a non-specific reference: it would give the sense that one might go with someone else's family. It would be fine here to say "one's family", though. (I don't think there's a nuance difference between the two because the class of potential families one might go the beach with is a class of one.)