I think that this is more of an over arching question than the world of golf. It runs up against the entire notion of visual literacy.
As to what do people notice, I have no way to generalize.
Sites such as Cape Kidnappers or PB are so overwhelming it is easy to overlook the course.
The late Mike Strantz makes you notice everything on the golf course.
No scholar of visual literacy am I. Just a golfer. I notice what's different. Normally my expectations of a course are based on what I've seen there before. If there's a change, I'll notice it. Or if there's something out of my ordinary experience, I'll notice. Then, sometimes, I'll see something somewhere that will strike me as so unusual, in my own experience, that I'll carry it over and ask, why don't we, they, whoever, do that (or, I'm really glad we don't do that)?
Then why ask the original question, "Do golfers really notice?" It has to do with how golfers are going to respond to the course for which you're responsible, public or private. It's marketing, isn't it? Bunkers and greens, as others have pointed out, by their nature . . . function . . . are going to be most likely to be noticed. From an operational standpoint, the question is how you can provide value -- the relatively best golf experience, as perceived by the golfers, for the least amount of money.
As a recreational golfer, I'd never really focused on the "bunker raking" issue until visiting Scotland. In my early golf experience, one carefully raked bunkers. You expected the grounds crew and other players to carefully rake bunkers. I had no real good idea why. That's just the way it was done. Professional golfers expect professionally raked bunkers. Seven years ago at Dornoch I found the bunkers unraked -- "smoothed" by foot, maybe. I cannot recall if rakes were even provided at Dornoch then. I recall courses in Scotland with old, beat-up-half-rakes, and some with fairly nice (American?) rakes. In neither case, however, used as carefully as normally the case here in the USA. Then, the idea of a bunker as a hazard started to take hold with me. Today, I could do with leaving the raking, with rakes, up to the players, or without rakes, up to the players with their clubs or feet, or whatever. But, from a marketing standpoint, I don't think that's going to work for the majority of players. You pay private club dues or public course fees, and you expect nicely raked bunkers (the pros do, of course, so shouldn't you?). If our club could save money by letting the golfers, on the go, do the raking, then, fine, as long as that's perceived by our members as good value in terms of money spent (on initiation and dues) and the end result -- bunkers that are hazards.
How do we get there? The way the economy is going, we may not have much choice. Otherwise, it's got to be a contest of wills. Those of us who prefer the hazard approach could push for that. At public courses the owners could just take chances. At private clubs, you'd be chance-taking too, but you could do it on an experimental basis. Let the players rake bunkers for a while, and see what happens. Announce that you're undertaking an experimental program and why (history or roots and money). Maybe the members will go for it, but maybe not. You'll never know unless you try. How about the PGA? Do they have the gumption to lead the way? No. Didn't Nicklaus try something with Oakmont style raking at the Memorial and get "killed" for it a number of years ago. Wouldn't it be cool if a rich man (or woman) put on a big dollar LPGA or PGA tournament without providing bunker rakes at all?
Mowing? I'm an intersted novice. Just a golfer. I'd like to have fairly consistent greens, not too fast and not too slow (by my definition!) for the slopes, but what kind of a mower? As a golfer, I have no idea what you're using and what the differences are. I'd like to learn, which is one of the reasons I've joined this group, but I am sure I'm in a very small minority of golfers in that respect.
Finally, focusing on the money-saving issue, in the private club setting, what about the members doing some of the work? I think that shoud be a separate discussion.