I've heard at least 2 theories that purport to explain that phenonemon.
1) The click happened right on the cusp of the date change, in which case the impression is on Tuesday and the click registered for Monday.
2) Clicks are reported on a more timely basis than impressions. Therefore, when you look, the click has updated the database, but the impression hasn't been logged yet.
There may be some other theories floating around too.
Personally I don't buy either one.
Theory #1 sounds like a tech-support guess. I don't blame them, I've given out the same type of implausible explanations to people.
Next, I've looked days later and I still had 1 click and 0 impressions which rules out #2.
This may be a bug and it could be much more prevalent than we realize. You only notice when the clicks exceed the impressions. How many impression-less clicks are buried in keyword stats that number in the tens or hundreds?
One thing I'm sure of: You'll be charged for the click :)
More ideas?
Israel
Don't call them my reasons ;) -- I'm just parroting what has been given as possible explanations to others on this board over the years.
I don't buy either one myself. Think it's a bug personally. I hate stuff like that too.
Okay, one more possibility:
If you search on +"1 click" +"0 impressions" +adwords, you can find some discussions that suggest this flaw occurs when one searches uses the region code in a search, usually another webmaster (perhaps yourself) checking for competition. That is, the &gl=cc where 'cc' is a country code.
Not sure I buy that either. Back to it being a bug then. However that should be the worst of Adwords' problems of late!
Israel
A bit worrying that the click from a fraudulent impression isn't filtered out though
If what Google claimed was true and indeed you didn't pay for the click, then you should consider it a bonus. You got a click without increasing impressions which helped your CTR in theory. Again, this is if you didn't pay for the click.
I see a small refund every month too. I doubt it represents the full value of the click fraud that I endure.
Admittedly, it's in everyone's best interests that Google not tell too much about how they "filter" out click fraud. However, I know it falls way, way short of catching all of it. I can see that just looking at the logs for a given site for a given day. Unfortunately, I can't make a full time job out of documenting it for Google. The best I can do is lower bids on the terms that I see repeatedly getting hit.
Israel