This is a topic I've been thinking about lately as I've been making an effort to see (and re-see) as much of Thompson's work as I can. Of course, I am limited because I can only see the golf courses as they lay today and do not know if they are as designed.
A few things I've noted...
1) Unbelievable micro-contouring in his flatter fairways
1b) Some of the most macro-contoured fairways I have ever seen. Interestingly, it seems Thompson liked the most wild terrain / extreme undulations to be an integral part of the hole. I feel some GCAs would have instead routed the course so that these areas were not in play, Thompson embraced them, adding a level of quirk and interest.
2) Thompson is a master is siting his greens (the best ever?). It is amazing how many times you play one of his holes and you say "yep, this is where the green should be." But there is so much variety. Even on a course no-one has ever heard of (Legacy Ridge FKA Owen Sound), his siting of greens was exceptional (even if green contours and sizes seem to have been dumbed down over the years).
3) Flair in bunkering. Ian noted that it was an evolution for Thompson to start designing the bunkers he is now so well-known for. But, I think that courses that are being restored are all being restored in that evolved Thompson style, whether or not that is how they were designed.
4) Visual deception with bunkering. I find most ODGs used their bunkers entirely with strategic intent. Not so with Thompson who likes to place bunkers (sometimes) in places that may have more of a visual effect than a strategic one. The bunkers short of the green on 1 and 2 at Burlington are two of the most cleverly placed I have ever seen.
5) Built-up greens. Again, Ian noted that this was an evolution for Thompson and I am sure he is right. Nonetheless, I have noted that most of his greens are pushed-up, many with falls-off on at least 2 sides and almost always at the rear...
6) Protecting the back of the green (ties into 5). On greens where there is no fall-off, there is often mounding. Thompson may have used the terrain to route his holes, find his greensites and design his fairways, but he wasn't afraid to move some dirt around the green.
7) Uphill walks between holes. In an era where short green to tee walks are commonplace, Thompson was not afraid to make his golfer trek a hill to reach the next tee. Obvious examples at Highlands Links, St George's, The Summit and Legacy Ridge.
That's it for now. Thoughts and corrections welcomed.
Edit: If there is interest I will add photos describing each of the above.