A more recent citation for time hierarchy theorems is "A Generic Time Hierarchy for Semantic Models With One Bit of Advice" by Dieter van Melkebeek and Konstantin Pervyshev that you can get from Dieter's webpage. The techniques there give a time hierarchy with 1 bit of advice for "any reasonable" semantic model of computing, including quantum algorithms.
Also, it is normally relatively easy to obtain a hierarchy for the promise problems computed by semantic models. A promise problem only requires an algorithm to "behave nicely" (e.g., have bounded error) on some inputs -- those that are chosen to be part of the promise problem. For inputs not chosen to be part of the promise, the algorithm can behave arbitrarily (e.g., not have bounded error). A hierarchy for promise problems is a folklore result; a proof for the BPP setting is given in "Space Hierarchy Results for Randomized and Other Semantic Models" by Dieter van Melkebeek and Jeff Kinne (myself) that you can get from Dieter's or my webpage. This should apply to quantum algorithms also.
So the answer is, decent hierarchy theorems are known for quantum algorithms that either get 1 bit of advice or are allowed to ignore problematic inputs. Some of the techniques for these results rely on the properties of randomized algorithms. It would be interesting to try and exploit the properties of quantum algorithms in the area of hierarchy theorems.
A somewhat related area where there are results specific to quantum algorithms is the area of time-space lower bounds. There is a survey by Dieter van Melkebeek: "A Survey of Lower Bounds for Satisfiability and Related Problems".