Yes, you can certainly request that a cab stops at the "Welcome" sign for a photo opp on your way to M Resort (we double checked with the Taxi Authority). Just be aware that you'll be charged the $30/hour "waiting time" rate for as long as you're there.
When it comes to a taxi stopping for you somewhere en route, that's fine; it's attempting to a cab from the curb that's ill-advised, for a number of reasons. On a practical level, they're all either loaded and going somewhere, or else on their way to a call, so they can't stop for you. Also, the TA stresses that cabbies shouldn't pick up "flags," which represent the highest percentage of cab robberies. If you do somehow manage to get one to stop, the driver should pull off the street so you can enter the cab safely.
Every hotel in Las Vegas, whether it's on the Strip, downtown, or out in the neighborhoods, has a taxi stand. If you're not at or near a hotel, the best way to get a cab is to call one. Just about every convenience store or bar will phone a cab company for you.
Even if you're at a hotel taxi stand, you may experience frustration after waiting for a cab for a long time, only to have one one pull in, unload, and leave without picking up a passenger. This isn't a case of the driver being rude or unhelpful: Check the rear fender and you'll see a red plaque denoting that the cab is "geographically restricted" and cannot pick up at the airport, the Strip, or downtown. (The Convention Center also used to be on the list, but that restriction was lifted in June, 2005.) This rule was introduced by the TA so that people away from those prime tourist areas still have a chance to get a cab.
