neighbor enter & realize I'm not there.? Can the cops just open a window and enter based on a neighbor's statement that I went missing and not seen by the neighbor?
Yes. They have an obligation to conduct a well-being check to ensure that you aren't dead...in which case you're beyond help...or injured...in which case you'd be pleased they showed up before you died and your dog made a meal out of you.
Like another poster said....you might want to let the neighbors know you're on vacation OR most PD's will conduct checks of your home if you call them and fill out a form stating you're on vacation and could they check your house on occasion.
I would think they should first try to look to see if your car was there. Then, they should try to call you on the phone, maybe call your other family members or your place of business. Maybe check credit or bank card activity. If you flew on a plane, the FAA should know.
They should look for other indicators as well. Are the lights on? Is the television on? Are pets home? Is the mail checked? Is the power meter moving? I suspect that there would be some odor if you were dead.
Personally, I don't think that heresay is grounds for invading your home, unless they tried several other routes beforehand.
Someone said the cops were acting in good faith. There are several viable channels to take before breaking into someone's house supposedly "in good faith".
Also, your neighbor should never have been allowed into your house regardless.
They can because they were acting on a tip in good faith, a tip that amounts to an exigent circumstance. If they found anything illicit while in your home, believe it or not, it would be legal as they were acting in good faith.
Now that I think about it, that's actually a really good indirect way to get someone's house raided haha.