I'd say one big disadvantage would be that you may never come out
ahead financially. I have a typical gas water heater, not high
efficiency, and in the summer, when it's the only gas load, my bill is
less than $20. And that includes actual water usage as well as the
standby losses, which obviously aren't very substantial..
You may also find that to get the right size tankless requires a
larger gas service, increasing gas pipe size from the meter to where
the tnakless is located, etc.
If you can, do a simple experiment sometime. When you're going to be
away for a few days to a week, record the gas meter reading, make sure
the water heater is the only usage, ie turn off any other pilot
lights, heat, etc., then read it again when you return. That will
tell you how much you are paying for standby losses.
And as others have pointed out, these losses can be cut down
substantially by going to a high eff gas tank water heater, which is
still typically a lot less than the install of a tankless. These
close off the exhaust vent when the burner is not running, which
substantially cuts the heat loss. I'd be looking at those when it's
time for a new water heater. However, one other thing to consider is
there is currently an energy tax credit in effect and some of these
solutions could get you a credit for up to 30% of the cost. If you
have a tank that is nearing the end of it's life, now may be the time
to replace it with something.