Hey this seems like somewhat of an easy way to poison someone; shoot them with a poison covered bullet! The problem would be that you couldn't kill them when you shoot them! What do you think?

I'm not sure I can see any advantage. Surely the only reason for adding poison is if the projectile is too light/slow to cause fatal injury by itself (such as poison darts)?

How do you intend to keep your victim from seeking medical assistance for the gunshot wound?

The "undetectable poison, unknown to science" is only found in mystery novels written by someone who couldn't come up with a halfway decent plot. If a wound isn't healing, or odd complications occur, the doctor is going to try to find out why, and has a good chance of finding out. At which point it's antitoxin time.

If the idea is to kill the person, why not skip the poison and just put a round through the skull?

If you're going to go to the trouble of shooting someone, why not make it a fatal shot? There are suppressed firearms out there that can fire a lethal shot that would go unnoticed in many situations.

Well, it worked for the Russians. The KGB did that fellow with Ricin inside a tiny metal ball only a couple of mm in diameter.

Not really a bullet...

Most shooters opt for "acute lead poisoning".

Replying to Antigones68104's comment, usually hospitals don't test gunshot victims for poisons such as arcenic (if that is how you spell that). Plus if the person did.. die, then a medical examiner would be less likely to search for a certain poison, if they were being lazy, and instead look for later infection.

I don't remember the exact details but a number of years ago, late 1970's I think, a political assignation by the KGB of a Bulgarian with the poison ricin in holes a small ball shot out of a spring loaded umbrella.