I have only seen War Games because the time I watched it, (about two years ago), all his episodes were either half restored or audio only. I really tried listening to just audio but it just isn't the same.
Pat Troughton stared in 21 stories over 3 years (1966-69), or around 110 half hour episodes. Of those, only 6 stories are completely intact: The Tomb of the Cybermen, The Krotons, The Dominators, The Mind Robber, The Seeds of Death, The War Games. These, plus The Ice Warriors and The Invasion (both missing 2 episodes) were all released on VHS in the 80's/90's. Often these VHS releases featured little restoration work, and some in particular were rather poor quality. They are now all available on DVD with vastly improved picture and audio, plus lots of extras.
There are about 13 "orphaned" episodes from Troughton's era - episodes that don't make a full story. These episodes are all available on the special "Lost in Time" box set DVD (inc Hartnell's orphan episodes too). Subject to the possible news this week, Lost in Time is a great buy if you enjoy this era of Doctor Who, as whilst you may not get the full story, there are some great moments on these orphaned episodes.
Yes, listening to a Doctor Who story that only exists as audio is very difficult... I LOVE Doctor Who, have done all my life, but even I have only listened to a small handful of the audios... (Incidentally - they exist thanks to several fans who recorded the audio tracks by placing a cassette recorder next to their TV, because they had to go to work/etc, but didn't want to miss the show. It's amazing that we have this option, that has now allowed the BBC to create animations to go with the audio tracks for stories that are missing only 1-2 episodes, and release them on DVD.)
I now see that some of his episodes are available like the Mind Robbers and the Dominators. I definitely want to watch those.
MR is a 10/10 for me... Dominators... 4/10... Still fun at times though.
Also, I'm not sure which episode the second Doctor meets the Brigadier because Brigadier mentions he met the Doctor before his third reincarnation. Maybe that episode is missing too. I'm going to try and find that episode and see if I can watch that.
Sadly, that first encounter between the Second Doctor and then Corporal Lethbridge-Stewart occurred late in The Web of Fear. Episode 1 of that story exists, but that is all... You can however watch The Invasion, which is the UNIT origin story, when Lethbridge-Stewart is re-introduced, now with the rank of Brigadier, and in charge of his own special team investigating alien invasions etc... The Invasion is missing 2 out of 8 of its episodes, but they have been brought back to life with the aforementioned animations with original soundtracks.
Also where can do you actually go to buy these? Maybe I can buy a DVD of the second Doctor's available episodes? I didn't see anything by searching the BBC website.
Some episodes are on iTunes... but other than that, they are certainly available in the US on DVD... Earlier (ie early 2000's) I think the DVDs took a while to reach the US, but now they are released within a few weeks of the UK release dates.
Amazon certainly has them... though - as a test I just tried finding "The Invasion", and Amazon want US$59! It's only AU$19 here in Australia...
http://www.amazon.com/Doctor-Who-In...381202907&sr=1-1&keywords=doctor+who+invasion
https://shop.abc.net.au/products/doctor-who-the-invasion-1
Looking at other titles, The Invasion must be rare or something, as usually you're only looking at US$20.
(Yes, Doctor Who is not cheap to buy, compared to other franchises, though these days you should be able to pick up stories for around $10 on eBay etc... )