"Hold your fire. There are no life forms. It must have been short-circuited"

Man, I bet the guy who didn't shoot the pod got Force Choked the next day...

 

It doesn't really make much sense does it? The inference is that if there had been life-forms in the pod, they would have fired. So "not vaporizing the plans" doesn't work - they could just as easily be in a manned pod. It's just a plot convenience - trading an obvious plot hole (why'd they let that pod go?) for a slightly less obvious one (oh, 'cause it had no life forms. Uh, waitaminute... Too late! - on to the next scene!)

As for why Vader didn't go down - he judged it more important (or was ordered by a higher power) to extract information about the Rebellion from the Princess - retrieving the plans was just a matter of time. He didn't count on two diligent droids, several smelly Jawas, one callow farmboy, his long-lost Master, and a couple of desperate smugglers to thwart his plans.

 

You may be drawing an assumption that isn't totally accurate. Any Sith would be trained in stalking enemies.
Ben: " He (Vader) helped the Empire hunt down and destroy the Jedi Knights."

You're right, Vader could track enemies.
But from the Empire's prospective the princess likely hid the plans in the escape pod since they weren't on the ship. Why would Lord Darth Vader go wandering across a desert to find an escape pod?
Even after droids were discovered Vader would have been no use in the search since droids can't be "felt" in the force.

The real question is: What was that round "droid thing" the troops found, and why don't R2 or 3P0 seem to miss it?

 

The Pod bugs me. Vader doesn't.

There's no particular reason for Vader himself to go. Just because he went down on Hoth and Endor doesn't mean the he went down to any plent he came across.
Also, you're forgetting a very important thing that was on Hoth and Endor to Vader. Luke
Why would Vader need to go pick up some plans? He had that whole Death Star thingamabob to watch over. Sending him to get plans seems like a waste of his skills when stormtroopers could easily do it. The pod was empty afterall right? That's what they thought.

PALPATINE: Lord Vader.

VADER: What is thy bidding, my master?

PALPATINE: Go into the unknown regions. There are reports that a planet still carries the Mc Rib. Get me one!

VADER: My master... is that a wise use of my power? There is a civil war going on.

PALPATINE: Pish posh! I want my Mc Rib dammit!

 

It would be better if a whole bunch of pods are falling and 1 or 2 of them get by.

 

Simple reason why Vader didn't go himself.He's a Dark Lord of the Sith not a mere errand boy.Leave the fetch quests to the insignifigant lackeys.