Should wildcard import be avoided?

There are also good cases for import *. ie. it's common for Django developers to have many config files and chain them using import *:

settings.py:
FOO = 1
BAR = 2
DEBUG = False

test_settings.py:
from settings import *
DEBUG = True

In this case most disadvantages of import * become advantages.

The answer to your question's title is "yes": I recommend never using from ... import *, and I discussed the reasons in another very recent answer. Briefly, qualified names are good, barenames are very limited, so the "third option" is optimal (as you'll be using qualified names, not barenames) among those you present.

(Advantages of qualified names wrt barenames include ease of faking/mocking for testing purposes, reduced to nullified risk of unnoticed errors induced by accidental rebinding, ability to "semi-fake" the top name in a "tracing class" for the purpose of logging exactly what you're using and easing such activities as profiling, and so forth -- disadvantages, just about none... see also the last-but-not-least koan in the Zen of Python, import this at the interactive interpreter prompt).

Equally good, if you grudge the 7 extra characters to say QtCore.whatever, is to abbreviate -- from PyQt4 import QtCore as Cr and from PyQt4 import QtGi as Gu (then use Cr.blah and Gu.zorp) or the like. Like all abbreviations, it's a style tradeoff between conciseness and clarity (would you rather name a variable count_of_all_widgets_in_the_inventory, num_widgets, or x? often the middle choice would be best, but not always;-).

BTW, I would not use more than one as clause in a single from or import statement (could be confusing), I'd rather have multiple statements (also easier to debug if any import is giving problem, to edit if you change your imports in the future, ...).