I’ve been watching these in the afternoon on CHCH the last couple of weeks. I realize that the series was recorded live in the studio almost 65 years ago, but the sound and (sometimes) the images are so bad, I have trouble following the stories. (The writing then could have been better too.)
Given the marvels of modern technology, can’t these episodes be cleaned up just a bit so I’m not straining to understand what’s going on?
I saw a few of these and don’t think it’s worth it. I didn’t find them entertaining at all.
On edit: As you said, the stories were not very good, I found the acting mannered and not with a sly wink as in the Emma Peel years that were fun without devolving into the utter silliness that was the Tara King years.
I think the Cathy Gale episodes were the best of the early ones. But then the production values were so low that’s not saying a lot. It’d be nice if better video of those episodes magically appeared. (AI video processing would have to get a lot cheaper, basically free, to make it worthwhile.)
The reuse of sets was sad. There was the Big Bad’s lair complete with metal spiral staircase, the skeevy shop, etc.
With the Emma Peel ones they had a deal with a US network so they had more money and it shows. But even then some of the plots were really corny. Esp. the “magic technology” ones.
1967’s “Mission: HIGHLY Improbable” will always be one of my favorites! 
EMMA: “Steed, is everything to scale?”
The only one of the Tara King episodes I even remember is “Stop Me If You’ve Heard This One,” with John Cleese and “Mr Hutchinson” from Fawlty Towers. That one is hilarious, probably because it’s based on clowns!
Speaking of MPFC, Carol Cleveland appeared in the infamous “A Touch of Brimstone” episode. (Which was still in the B&W era.)
Another of my favorites:
The added music is really intrusive and annoying in that clip.
Can kinescopes be remastered?
The images and sound can be cleaned up, I would imagine. Not perfect, certainly, but better than they are now. They’ve already been transferred to DVDs or some other modern medium.
Turns out they have been remastered, according to Wikipedia. But if they’re the episodes I’ve been watching on weekdays lately, the quality is still not good:
From the late 1990s to the early 2000s, A&E TV Home Entertainment (under license from Canal+ Image International) released the remaining surviving series on Region 1 DVD in North America, with newly remastered picture and sound quality.
Series 4, 5 and 6 were remastered and released on Blu-ray by Studio Canal.
UPDATE: Colorized episodes from Seasons 1–3 are available at Internet Archive. I’ve only had a quick look so far, but the quality overall is vastly superior to the B&W episodes I’ve been watching in the afternoon. You can actually see and hear what’s going on, and the sets are more than just dark shadows.
I know some Emma Peel episodes are available as well, but I haven’t had time to explore further.
The move to film from VT (and eventually colour, even though British TV wouldn’t broadcast them in colour until the 1970s) is the only thing that keeps The Avengers watchable.
Elstree was a poverty-stricken studio, like most of the British film industry in the 1960s, and recycling of props and costumes was a given.
The picture quality was good enough for the 405-line TVs most people would have been watching them on at the time.