I'm a native English speaker and I've never been able to really parse this one. Is it a command aimed at the police? If so, shouldn't it be "police, take notice"? Is this construction used anywhere except these kind of signs?
It's a sign which informs the police that the property in question is privately owned and any person or persons trespassing aren't supposed to be there. The sign also gives the police the freedom to enter the property and remove any such persons if necessary without the direct approval of the owner, as the approval is implied in the sign.
And thus, the sign is there to inform the public that they cannot trespass and that the police take notice over how this sign is respected. The sign is correct and no comma is missing.
I agree this is odd, and bad grammar no matter what it means. My understanding of these signs is that they are required in many places in order for the police to be able to enforce protection of private property without the invitation of the property owner.
Ie, where the local laws are written this way:
Pretend you own a large field, and someone is camping in the back of it.
If you have a sign that says "no trespassing" or "no camping, police take notice", the sign is granting permission for the police to come onto your property and see who is camping back there.
If you do NOT have a sign, then the police would not be allowed to enter your property unless you invited them -- for instance, by calling them and saying "somebody is camping in my field! help!"
I'm pretty sure that's what the signs mean, but you're right about the grammar being incorrect.
It is effectively saying "The police do/will take notice". It's similar to you saying "Dogs run". It's a statement of fact.
I have never seen such a sign in the US and it certainly is grammatically incorrect. If it is commanding the police to take notice, then it should have a colon. If it is informing that the police do take notice, then it is missing the article ( the ) and the verb ( do ).