The vast majority of the "problems" people cite with LCDs (unsuitable aspect ratio, input delay or "lag", viewing angles, fixed refresh rate, bad colors, and probably some others I'm not remembering right now) can be solved by buying a good (not just overall quality but also suitable for this particular purpose) LCD. We're already starting to see dedicated arcade LCDs hit the market, and as these see more development, it's possible we'll see the support electronics develop to cater to the peculiar needs of this market. There's nothing inherent in the LCD technology itself that causes these problems; it's simply the nature of the available panels as well as the support electronics that are generally made for television and PC monitor applications.
Unfortunately, "good" LCDs are hard to find since the specs you care about in this application are rarely published in any accurate or detailed form, and when you finally find one, it's bound to be fairly expensive (think $500+ for a ~20"). Given that you can buy an honest to god arcade monitor for about this price, that kinda puts a damper on the enthusiasm for going LCD, aside from the fact that they're smaller. As CRTs become harder to find new and LCDs continue to be refined, this tradeoff may shift. I'm not sure any manufacturer is still making the actual CRTs (bare tubes); all that's left are new old stock that are being put into the arcade monitors still on the market.
One thing you can't get around is the need to scale, since no panels are made at the sizes desired in the low resolutions the old games used, and, even if they were, you'd need a separate panel for each game, or you'd have to put up with small bars surrounding the game on the lower res stuff. Fortunately, the relatively high resolution allows you to scale with some neat effects like the HLSL effects already mentioned. A naieve bilinear or similar scale will indeed look pretty ugly in this application. Hopefully, the MAME HLSL effects may eventually get tweaked enough to provide a good experience on a "good" LCD (see above). They already look pretty impressive.
Now, none of this is to say I'm an LCD fan. I'm not, at least when it comes to gaming. Every arcade game I own has a CRT on it except for my beatmaniaIIDX which has a plasma as CRTs at 40-42" 16:9 were never made (the original monitor was an LCD projection set that died long before I acquired the cabinet and was problematic in other ways, anyway). I even "stock" several new-in-box arcade monitors for the inevitable death of some of the ones in my games, and I repair whenever I can. My PC gaming setup uses 3x24" widescreen CRTs. I love the look of a good CRT, but I'm not going to be oblivious to the fact that they're going to be essentially impossible to get new within a few years.