There's a discussion of bugs in CAS's here, but these are technical errors of interest mainly to the professional mathematician. I am more interested in simple errors which might arise in the use of CAS for undergraduate teaching. For example, if we were asked to compute
$$\int x(1+x)^{19}\,dx$$
say, we would use integration by parts and end up with
$$\frac{1}{20}x(1+x)^{20}-\frac{1}{420}(1+x)^{21}+C$$
which is neat, and clearly easily generalizable to any power. However, your CAS, given this problem, is likely to think: "Aha! products of powers of polynomials!", expand the integrand into powers of $x$ and integrate the result term by term. The result is not formally wrong, but it is confusing, and from the point of view of elementary teaching, useless.
Does anybody know of other examples where a CAS (or CAS calculator like the TI-Nspire, the Casio ClassPad, or the HP Prime), gives an answer which is either wrong, or in a form which is useless?
Pick your favorite expression that is zero but not easily simplified to zero by the CAS. Then divide by this zero and deduce all kinds of absurdities.
Another place a CAS go wrong is properly dealing with branch cuts, and keeping track of domains of validity for various expressions.
These and other problems have been discussed in the literature. A good place to find such information is to browse the web pages of leading researchers, and conference proceedings (ISSAC,SYMSAC,Sigsam,Eurosam, etc). For example, see Richard Fateman's papers, e.g. his 33 page critique of Mathematica, and Why Computer Algebra Systems Can't Solve Simple Equations and Branch Cuts in Computer Algebra, etc.