I'm not entirely sure when this issue started for me but I know it's been since 11-Oct-2012. I'm always on the latest iTunes so if you know release dates you'll know what version it started for me. The HD TV show downloaded from iTunes didn't have Album Artwork. It was irritating but dismissed it. November&December 2012 I purchased several new releases in HD. None of them displayed the Album Artwork on any of my devices (MacbookPro, iPhone, AppleTV). I'm currently on iTunes 11.0.1. As already pointed out you can paste a new photo into "Get Info==>Artwork tab" hit save but it DOESN't save. You can select "Get Album Artwork" but it doesn't produce anything. Now in my trial-and-error phase I tried deleting the Movie from my MacbookPro and re-downloading through the cloud. It worked. I had Album Artwork. Unfortunetly, the iTunes Extra didn't download which frankly ticked me off as well. I tried the delete, re-download process again and it downloaded everything but again NO Album Artwork. It's important to mention that the iTunes Extra file does contain the Album Artwork and even after "linking" the movie with the extras by "part of a compilation, 1 of 2 and 2 of 2" it didn't fix the Artwork problem. So, I think the problem is when the actual download from iTunes store and how it saves to the iTunes Media Library. And, yes, I'm on a NAS device. Regardless, here is the workaround that resolved all 6 movies and 1 TV show. The solution is manually adding the movie into iTunes and not relying on the download from the cloud.
Fix
Step 1; copy individual movie folder such as "Brave" to another directory outside of iTunes Media Folder <note: in recent iTunes you'll notice all files, HD, SD and Extra is in one folder - NOT always the case with older versons>
Step 2: delete move from iTunes desktop but select "keep files"
Step 3: rename the movie folder of the movie you just deleted within iTunes Desktop
Step 4: in iTunes desktop, select from File menu, "Add to Library" and select the copied folder from Step 1; e.g. the one outside of the iTunes Media Folder
Step 5: once import is complete, verify Artwork is now as it should be displayed
Step 6: verify the movie folder back into iTunes Media Folder <if it is not but the movie was added, check advanced tab within preferences and check the box to add files to iTunes Media Folder on import>
Step 7: delete copied movie folder that you placed outside iTunes Media Folder from step 1
Step 8: delete the renamed, original, movie folder from step 3
Optional: iTunes at some point listed the movie and iTunes Extras as compilations. I found I had problems in the past if it wasn't linked. So, I manually make the movie part 1 of 2 and the iTunes extra part 2 of 2. Don't forget to hit the compilation flag too.