This review contains moderate spoilers.
I certainly wouldn't rank this as one of my all-time favourite 'Star Trek' episodes, but for what is essentially a ship-based 'bottle show', it actually has some interesting elements; and I actually found myself thinking about it a lot after it had finished, which is surely a good sign.
This is one of a handful of Original 'Trek' episodes set entirely aboard the Enterprise. But unlike later 'Trek' spin-off series, where there were very often (cost cutting) ship-bound stories, and often where nothing much really happened, those in the Original Series often turn out to be very good, as previous examples "Charlie X" and the classic "Balance of Terror" prove.
Nomad is an interesting design, and rightly not resembling the human form at all. In a way its design reminded me of the Daleks from 'Doctor Who'; if it had resembled a human form, I think it would have taken away much of its mystery.
No doubt if this episode was produced 30+ years later, Nomad would be CGI, but here, in the era of more conventional special effects, it is moved around manually, often with its top or bottom conveniently out of camera shot (no doubt for something to hold on to it and move it around!).
As has already been much commented, Nomad is very similar to V'Ger in 'Star Trek: The (Slow) Motion Picture' (1979). Out of the two, this is by far the better story (at least it's not as incredibly dragged out as TMP, arguably the weakest of the big-screen outings).
One good sequence is as Spock mind-melds with Nomad, only to get 'stuck' in Nomad's thoughts. What could have easily have fallen into an unintentionally amusing moment is actually performed quite well. (I wasn't sure about Spock actually being able to mind-meld with a machine; something that doesn't think for itself and is programmed a certain way, but this was only a very small niggle).
I wasn't convinced by Uhura's 're-education' after her mind was wiped by Nomad. Are we really expected to believe that she would totally relearn and regain everything she knew before? What about her memories and such? This was the weakest point of the story for me. Personally I like to explain it away as her 're-education' triggering her past memories and such over time. (In fact, it would have been cool if they turned her re-learning into a story arc, but sadly such things didn't exist in the Original Series, where stories were very much 'stand alone' tales).
In the end, Captain Kirk once again 'out thinks' the computer, causing it to self-destruct. It had already been done in the first season in "The Return of the Archons", and with an android in "What Are Little Girls Made Of?", and he pulls the trick again here. It is still a good scene though.
All-in-all, this is a bit of a strange one to sum up. It's not a series classic, and not one of my favourite episodes, but it does have a number of good things going for it.