Here are some initial thoughts. Sorry if it's too long.
In terms of graphics, Luigi's Mansion has aged very, very well, especially considering that it was a launch title for the Cube. I love the effects of Luigi's flashlight, and the colorful, glowing, ethereal quality of all the ghosts, which, oddly, are probably the most bright and colorful element of the game. Aside from the boos, they all sort of reminded me of the Haunted Mansion at Disney World for some reason. The object physics also deserve some mention... I love the way that you can pull tablecloths and curtains with the vacuum; very few games still bother with this sort of thing.
There is mild Mario-type dry humor lightly sprinkled throughout the game, such as the Gameboy Horror, some of the game's diaglog, and some of the easter eggs hidden in the mansion. I smiled when I tried to vacuum off the movie screen in the Projector Room and was rewarded with an image on the screen that showed a Boo and red text that said "Get out of here!" I went around in the mansion just inspecting things with the Gameboy Horror; once when I looked at a toilet in the washroom, Luigi's response was, "Boy, those boos sure built a realistic fake mansion."
The game also oozes character and charm. I love the little touches they added, such as the shaking in Luigi's hand as he opens a door to an unfamiliar room, Luigi's icy breath when he is in a haunted area (a reference to the Sixth Sense, perhaps?), or the subtle changes in Luigi's expressions and gait when all the ghosts in an area have been defeated. Who hasn't smiled at least once when they hear Luigi shakily humming or happily whistling along with the game music? I also love that you can choose to have Luigi call out for Mario, though I was disappointed when I found out that didn't really serve a purpose in the game. Anyway, that's why I still love this game, despite it's flaws: you can tell that it was carefully designed and crafted.
The controls are a mixed bag. On one hand, capturing most of the ghosts, such as the normal mansion ghosts, and the ghosts from the paintings, feels great. This seems to be because you can sort of lock onto the ghosts with the vacuum, and you have to sort of pull back on the control stick in order to capture them. It sort of gives you the feeling that you are really struggling with the ghosts. On the other hand, when that locking mechanism is downplayed, I found that controlling Luigi's vaccum with the C-stick was a bit sluggish and inaccurate. This was particularly evident to me in the fight with the third boss, Boolossus; I had more trouble than I should have in aiming at all the boos floating around, at least when there weren't as many targets to shoot. Also, capturing some of the boos hidden throughout the mansion could be a real pain since that locking mechanism didn't work as well on them; I often found myself struggling to aim the vaccum in the right direction before they slipped into another room. This probably just means I suck at using the vacuum.
On the whole, Luigi seems a bit stiff, slow, and very grounded. This is a problem when the game seems to sell itself as being in the Mario universe, particularly given that, up to that point, fans could usually expect a Mario-style game to launch with each iteration of Nintendo hardware. Mostly, in a Mario style game you can expect to run, jump around, and explore, but Luigi's Mansion just couldn't live up to those expectations given the way it was designed. Before I read the previews and early reviews of the game, I was hoping for something more along the lines of an extended Haunted House in Mario 64, albiet with more puzzle solving. This was all the more sort of a thumb in the eye for long-time Luigi fans such as myself, because we're the nerds who had wanted to be able to play as Luigi in Mario 64. We finally got a game featuring Luigi, and it wasn't exactly what most of us wanted.
All that being said, I wish that Nintendo would release a sequel to this game with motion controls or add the existing game to the New Play control! series. I think it would have been a good fit, but I'm not sure how well it would sell. I'm sure there are a lot of Wii owners who never experienced Luigi's Mansion that would buy it, though.