Peeping through a window is a search though. I have a case in my head but can't remember it. It dealt with if a person is an overnight guest, they have no expectation of privacy in what is seen through a window, but residents do?
I'll try to remember it.
If grenades were seen, that is basically an arsenal, and yes, exigency permits a home arrest without a warrant. That does mean the charge will stand if it is a defacto UNconstitutional search though.
Edit:
Here is the case, and the ovenight guest does have an expectation of privacy, I got it backed up.
http://www.law.cornell.edu/supct/html/97-1147.ZS.html

