From where I see it, the main disadvandage of a high-zoom P&S is the sensor size. Any P&S camera (aside from the Sigma DP-1) has a very small sensor size compared to even the Olympus crop sensors (that are smaller than Nikon & Canon crop sensors). This leads to many other problems, such as much more image noise, both from long exposures and high ISO values, less detail in photos, lack of sharpness, etc etc.
There are other problems with P&Ss too, like shutter lag (my old P&S had a 1-second lag!), a VERY bad lens (compared to a DSLR's lens, at least), and other issues.
However, before you jump into photography, be aware that it isn't a one-off payment of
X pounds/dollars and you're set. Oh, no. There's a camera bag, a memory card, maybe a tripod, probably another lens or two, and that's just what most people on TPF count as the "essentials"!

My dad made that mistake and ended up giving me another 50-odd quid's worth of stuff

.
Just be aware, there is SO much stuff you can buy you can sometimes feel like your stuff is inadequate, but there's nothing that will improve your photographs more than your skill.