I am house-sitting, and taking care of their dog. He has started to urinate everywhere and is humping people. He is also panting more than usual. Is this an emergency? Should I take him to the vet?

How old is the dog? Is the dog just peeing unknowingly, or is he going around and marking territory? Finally, has the dog had the operation?

there may be a dog in heat near by.

Has he been 'dogsat' before?
Is it out of character?
It could just be separation anxiety.
How long do you have him for? He might settle down in a day or two.
I sat for a dalmation for 4 weeks once!
The first 3 days were a nightmare, jumping up at everyone, trying to hump me all the time!!
I just took control and acted as pack leader for that time, he then obeyed my commands and settled down, he just wanted to know what to do.
I even managed to teach him recall...his owners were amazed!