Here's another device that adds some complexity to anagram clues: more than one word/phrase in the clue that could act as anagrind.
Look at this:
THC 9353 (Gridman): Order tinned mixture (6)
The fodder is "tinned" all right, but which is the indicator, which the definition? Is the answer a word that means "order", or one that means "mixture"?
The setter cannot omit the anagrind, and must put it adjacent to the fodder - that's a given - but the anagrind could appear to the left or the right of the fodder. If the setter pads both sides of the fodder with anagrind-type words, the solver is at least briefly confused about which to consider the definition. The anagram clue is not so simple anymore.
Another similarly structured clue:
Times 23469: Having drunk rum, becomes awkward (10)
And a variant in which the definition is clear enough, the difficulty is in differentiating between the indicator and the fodder:
Times 24055: Pedal machine that's ineptly altered (7)