Do you agree: limit(ABS(x)^n,n,∞,1); => undef (One-sided limit: n≥0)

[parisse]

Limits at infinity should use the syntax limit(expression,variable,inf) for +infinity or -inf for -infinity, there is no support for sided-limit at infinity because there is no need to.
As Arno K explained, the limit of abs(x)^n at n=+infinity depends on x, you must make assumptions otherwise you get undef.
0^n is undefined, and 0^n is evaluated before the limit in limit(0^n,n,inf). You can quote to prevent evaluation. Of course that's not really the kind of computation that I run with a CAS :-)