Adventure games are all about exploring your environment. You point, you click, and you get a description, or a comment, or the character performs any myriad of actions (you hope.) In good adventure games, you'll get some sort of response. In bad adventure games, that response will be "that doesn't work," or "I don't see anything special." In terrible adventure games, you won't even be given the opportunity to get a response.
In my opinion, possibly the biggest sin committed in an adventure game is a lack of interactivity. Let's say you enter a room that is decorated with all sorts of interesting items, but the only one you can interact with is the one you actually need to progress. How frustrating is that? I want to look at the oddly-shaped lamp, even if I just get some jokey description of it!
Now, to play Devil's advocate, too many hotspots can also be confusing. This opens the door to pixel hunting, which nobody likes, and often times can be overwhelming for the player. Like everything else, the trick is to find that proper balance. Personally, I usually try for 10 hotspots or less per room, but I always try to have more than 4. It all depends on your environment, of course, but often times things can be consolidated.
For instance, if you have a fantasy game with a room full of treasure, and your background drawing shows gold coins, chests, rubies, scepters, etc, it would be unfair to the player if the only available hotspot was "treasure." On the other hand, if you made a separate hotspot for "coins," "rubies," diamonds," "scepters," and every object in the pile, it might be too much, especially if you need to take one specific item of treasure. You'd be fine with "coins" and "trinkets," with maybe "baubles" thrown in for good measure, and in your description mention the individual bits.
I'm going to call out one game in particular which suffers from both problems I have mentioned. Said game is Runaway: A Road Adventure. This game is drawn in lovely high resolution with backgrounds that are jam-packed with detail. In some backgrounds, there are entirely too many hotspots. At other times, hotspots won't appear among the already too many until the player finds out he needs something (which is an entirely different subject.)
Then you have backgrounds like this one:
Look at all that interesting stuff! A well, a skeleton, some weird saint on the wall, a painting, a chicken on a dresser, a stuffed owl. I could go on all day. Do you know how many of these items the game allows you to interact with? Go on, guess. Do you give up? Ok, I'll tell you.
That's right. This room is only used for cutscene purposes. You walk in, the creepy lady tells you she needs something, you walk right back out. You never once have control of the player in this room. You have no idea how much that irritated me. It was just one more strike of many others against this game.
In any case, take heed developers: let your player interact with your world. Not only is it fun, but it adds to the immersion like you wouldn't believe.