If I say time is the fourth dimension am I wrong? As far as I know the prevailing view is that time is the fourth dimension, but I've read there is also a spatial fourth dimension and even higher spatial dimensions after that so I hesitate to say that time is the fourth dimension. So, if I say time is the fourth dimension am I wrong?
 A: The "sort" of dimensions is really arbitrary.
What is true is that in classical mechanics time is another label to distinguish events, and special relativity enhances this point of view because there are some reference transformation that "mix" time with space (they are Lorentz transformations).
In general relativity there are more reference transformations allowed, and time is more indistinguishable (only locally you can identify the time "direction"), and it puts in the idea of curved spacetime. In this framework is possible interpret the curvature of spacetime as we live in a curved hypersurface of a 4D space.
So the fourth space dimension in this framework is fictitious: imagine to live in 2D on the surface of a sphere, you are 2D, but the sphere is embedded in a 3D space.
Finally, if you don't consider any more complicated theory you live in a 4D spacetime: 3 space dimensions and 1 temporal.
A: Whatever you say you are almost certainly wrong (this is nothing personal). If history teaches us anything, it is that (despite our tendancy to be enamoured with our more recent achievements) any given theory is sooner or later proven to some extent "wrong". 
Probably including that one, (but neglect that for now :-) )
Anyway I suppose a less pedantic answer would be that if a theory is useful, then its paradigms are supportable, at least in its area of application. General Realtivity, in which time is treated as a 4th dimension is pretty useful, for example. 
Clearly, though, there is more to time than just the dimensional aspect - a proper understanding requires consideration of "the flow of time" - the relative rates of interactions between particles in this hypothesised temporal dimension, and of entropy and its relevance to the irreversibility of time.
A: You can invent any number of mathematical spaces. There's no reason why time can't be the first dimension of the one you invent, nor why it couldn't be the seventh or that you just have no time dimensions, and infinite other dimensions.
All that matters for whether it makes physical sense to do so or not is whether you can use it to obtain useful [and hopefully at some point falsifiable] results.
