I've got an 05 Avalon with 180,000 miles. Runs like a champ and have only had three problems with it since we bought it new.
1. Nav control panel cover fitment (makes it hard to open, replaced twice by dealer still coming apart)
2. Vvts tube failure (paid for new one before recall and got re-imbursed by Toyota)
3. Coil pack died (Easy fix happened at 120k miles)
Now I'm getting a moderate shaking/shuddering from front end through the steering wheel and shaking the car (like warped rotors when braking, but only does it on accel) during accelleration. Engine revs fine, plenty of power. No check engine light or any other lights. I've checked mounts, wheel bearings, joints, axles, rotors, subframe bolts and can't find any play in anything.
It's got me baffled.

Any one experience this or have any ideas?