Yes, this episode is borderline on campy, and even the writing has Kirk saying "up until now it's all been fun" to justify the more serious turn...
But the actors ensure it doesn't become camp.
As always, Roger C Carmel excels as Mudd - who needed an episode in the third season, with writers that could work with his strengths (since "Mudd's Women" is the more powerful and more effective episode). His scenes with his wife Stella, immortalized in android form as instructed by his definition of her to the other androids, are definitely right out of 1950s humor, and one cannot help but to feel sorry for her - even if she's an android! What compelled her to marry Mudd in the first place, since she ends up calling him a good-for-nothing drunk all the time? His rogue charm?
Kirk presses Mudd for an explanation over the lack of male androids, and Mudd is clearly stammering. Especially given how big Norman's "power cable" is behind the budget-saving sweatpants, more male androids are clearly needed. :)
In many ways, it should be given a lower score, but the actors are definitely having enough fun with it to make it a memorable-in-a-good-way episode.
Not to mention the base plot of "computers taking over humans", which is a running theme in TOS's tenure.
Get out a bottle of wine, a couple of friends, and enjoy. But the only thing you should take seriously is the CGI they put in - that looks great, especially how they replaced Norman's chest unit with blinky lights instead of an old gearbox... impressive stuff. Especially on blu-ray, and the budget accorded.