ok, first off, it depends on the nature of the flat spot... if it's from normal everyday commuting wear, it'll be fine as long as 3/32 is showing on the tread depth gauge... If it's a flat-spot from a previous owner who did burnouts, replace it. Easy ways to tell the difference, a burn-out tire will have slight bluing on the edges of the flat spot, from the heat cycles of the tire... also, it's a good bet that it's a burn-out tire if there is liquefied rubber stuck to the undertail tray and the rear shock... that stuff is a PAIN to clean off...
If it's not a burn-out tire, you can run it in the mountains no problem as long as 3/32 is showing. Turn in will feel funny, as the initial effort to get the bike off center will be much greater than normal... also, once the bike is off center, it'll feel fine while there, but may feel odd coming back to upright.... depending on how wide the flat spot is, the bike may feel odd at mid-lean angles, and it might not like following the correct line.... you can "ride through" these problems... and when you get a new tire, it'll feel like a completely different bike...
Bottom line, do what you're comfortable with. If you're not comfortable on this tire, your riding will show that... you won't enjoy riding as much as normal... if you can get comfortable with the idea of riding on it, you will be able to adjust to it, and get some decent usage out of it.