No harm, no foul, a laugh and slap on the back when you find it out? Or do you charge him with obstruction? It's your decision. I bet it matters if you personally like the liar.
This is what is pissing off the civilians...the imbalance of power. You can lie like a rug to beat the band, but a little person cannot, not even about little things. It gets worse: Contrary to what you've been implying, a cop will lie on the stand, under oath, if he needs to in order to obtain a conviction. I've known people who have worked in courts daily as support personnel, and they've seen it so you cannot deny it happens.
Rule of thumb about Judges: A Judge who used to be a defender will lean to the prosecution because he's sure the defendant is lying. A former prosecutor will lean to the defense because he knows the cop is probably lying. And you wonder why you get a lot of skepticism?
That is abroad sweeping assumption and I admit no such thing, other than you are guilty of assuming.
There were various options available to me when people lied. If they were already charged with something, and lied to me, I documented it and filed the paperwork with the case. Some situations resulted in an arrest for lying when there was no charge or pending charge. Sometimes I just laughed and ignored it.
It's unfortunate that there are cops who lie on the stand. When I lost cases, it made me a better investigator, and lying was never an option to win a case.
But since you are so jaded about the whole justice system, how would you change it to make it acceptable to you?