The AI seems to prioritize:

-Lands over artifacts
-Sources of colored mana over sources of colorless mana
-Sources which could produce multiple types of mana over single type sources

This creates strange situations when you double-click on cards and has caused me to end up unable to cast spells I otherwise could.

1) It will tap a dual land instead of a mox/basic land to pay for Sol Ring, for example.
2) It will tap any number of dual lands instead of a mox/basic land and a sol ring
3) I have a dual land and a land/mox which produces either U or G. If I cast an UG spell (cc:UG, 2/2 Flying) it will tap the dual land first and pull up a prompt asking me which type of mana I want to use. This is silly, because if it tapped the single color source first it wouldn't ask me, and not only would it be faster, but mistakes couldn't happen - and they did, I occasionally couldn't pay for the spell once I selected the worn color.
4) I have a sol ring out and 4 lands. I have a 2GG and an UG spell and enough sources of mana to cast both. If I double tap the 4 mana spell, the UI will tap all the lands and I wouldn't be able to cast the UG spell.

Etc. I've observed this over and over during the lenght of a playthrough. The process by which the engine selects which sources to prioritize should be looked into.

It should probably try to use any colorless sources over colored ones to pay for colorless first, then any mono-colored sources to pay for colored mana, and only then move on to colored sources for any remaining colored mana. I think.

EDIT: Another thing that just happend was 3 Islands and a Forest, autotap a 2cc artifact to see what happens, engine taps the island and the forest. Things like that seem to happen a lot.