In S01E06, Pycelle advises Ned Stark to wait until King Robert returns from his hunt before passing judgment on Gregor Clegane. Ned ignores him, sentences Gregor to death, and summons Tywin Lannister to King's Landing to answer for his bannerman's crimes.

I think Pycelle's advice was excellent, regardless of his loyalty to the Lannisters. There was no compelling reason to immediately sentence Gregor Clegane to death, much less threaten Tywin Lannister with being declared an enemy of the Crown.

Ned was effectively provoking a confrontation with one of the most powerful men in Westeros while the king was absent. Waiting for Robert would have made much more sense. If Robert agreed with Ned, the decision would have carried the king's personal authority, making it considerably harder for Tywin to challenge. If Robert disagreed, Ned would at least have avoided committing the Crown to a confrontation that the king himself was unwilling to pursue.