Urinating by water bowl

In brief: it is not so unusual for dogs to urinate close to, or even into, where they drink. If you ever have seen water loving breeds, say labrador retrievers, you will notice that many of them do not mind at all of urinating into a puddle at one end, while drinking from it at the other.

I would not worry too much about it. Make sure your dog gets regular potty time, and I am certain there will be no problems.

Why is your dog unneutered?  Urine marking is much less common in neutered dogs. 
There's no such thing as an "accident" (except if a dog is incontinent or ill).  A dog is either housebroken or he isn't.  A dog that marks indoors is not housebroken.  So, you have a couple of options.  Go back to Housebreaking 101 ("Way to Go - How to Housetrain a Dog of Any Age" by Patricia McConnell), or you neuter him and hope it diminishes the marking behavior (sometimes it doesn't, which is one reason I advocate pets be neutered if the owners don't plan to show the dog).

Thank you for your comments. I apologize for my own belated response as i didn't realize there were replies.

The dog isn't neutered yet because the shelter from which he was rescued has made an appointment with the ASPCA to do it. It should be taken care of within the next month.

It has happened again since my original post. On a couple of recent very cold nights, I put the kitten in the kitchen. Also last night I had a dogwalker drop by to meet him. He did not take to her at all! He headed straight for his crate, turned around and barked constantly. I walked him after she left although he didn't urinate. He urinated in the kitchen a couple of hours later while I was in the bathroom. Maybe he saw these 2 events as encroachments on his territory (even though the dogwalker did not go into the kitchen)?

I don't know, maybe I'm way off here, but could he have a urinary infection or a bladder infection??

Hello there []

First off, I don't think you need to explain if your dog is neutered or is going to be neutered. Whatever you do is fine, as long as you are willing and able to take on all ensuing responsibilities (kind of like it ought to be with people [] ) and do make sure that your dog does not bother other people or dogs because of his being not neutered. You do what you feel is right for you and your dog.

Secondly, I would want to warn you: do not let this become a pattern! You must make sure that you now catch the dog every single time it tries to eliminate indoors, interrupt it as gently as possible, and bring it outside. If you cannot watch the dog at all times, use a crate. Trying to come up with post factum 'explanations' is very human, but not very helpful in many cases. The dog needs to learn that eliminating inside is always 'wrong', no matter for what reason he might think otherwise.

Lastly, when the dog is outside, start training him to eliminate on cue. This is pretty easy: watch the dog closely, and when you see that he is going to go within the next seconds, you say your cue "Buster, go pee!" or whatever. Once he does, you praise (click, if he is clicker trained) and treat. The dog will quickly learn that by doing his thing when you tell him to, he earns nice rewards. Very convenient in many circumstances, and an empty bladder is tough to have accidents with. [] (Of course, rule out a health problem before anything else.)

Good luck!

The reason I asked why the dog was not neutered is to determine if part of my advice would be to go ahead and do so.  Obviously, if this dog was headed for the breed ring, I would not be telling someone to neuter to stop a possible marking problem.
 
The fact that the dog was able to have an "accident" while you were in another room makes it obvious that if you can't be right there to watch him (preferably with him tethered to you) then perhaps you should crate him.  Also, all dogs are capable of retaining some urine for the express purpose of marking, so if he's doing that, you will not solve your problem by making sure you take him out often enough.  If it is a UTI, that's easy to check for by taking a sample to your dog's vet for analysis. 
Since he will be neutered, that may help some, but not all neutered dogs stop marking behaviors once they start.  I think diligent housetraining will be your best defense against this behavior.