CT Why didn't Vader keep an eye on frozen Han?

Sidious was all over the place with regard to Luke before Luke surrendered to Vader in ROTJ. He initially wanted him to die. Mara Jade was involved. But he settled on turning him later. He also consulted the Prophets of the Dark Side concurrently. Vader wanted to obtain Luke, but he was also focused on business. I don't think that Vader gave a rat's posterior about Han.

 

I agree. I think Vader considered Han as Boba's project, and Vader had his interests elsewhere.

 

I think Vader had very little interest in Han, and only used him as bait to lure out Luke. I believe that Vader was confident that he'd meet with Luke again, so he wasn't overwhelmed with urgency.

 

I concur. Vader just wanted to use Han as a tool. He even refers to Han and those on the Falcon as "minor criminals" before he Force-chokes Needa. Not sure why he would call Leia a "minor criminal," but I think he's grouping Han and Chewie together. Perhaps he didn't want to tell the Imperial officers that Leia was with Han, since his personal objective is to capture Luke and he doesn't want them to become distracted.

"They are minor criminals! Marginal outlaws! You are inept!"
"N-no—Lord Vader—please…"
"And ineptitude is of no use to me or the Empire."

 

^^ From an earlier screenplay draft!

The final "apology accepted, Captain Needa" was a last minute voice addition in post-production , IIRC.

 

"and now I sense you wish to continue your search for young Skywalker"

I think after Empire Strikes Back, Vader was busy with preparing the new death star and diverted his plan to seek out Skywalker until ROTJ.