Started happening recently, I notice a severe shudder when I hit about 60-65 which seems to disappear when I reach 80. At one point, I thought one of the damn wheels is about to fall off.
I'm not entirely sure what to make of it; the only thing I can think of is that wheels may need to be balanced. Is there anything else I should look into?

 

alignment might help my moms car did he same thing balanced rotated and aligned and t stoped

 

alignment and wheel balance.

 

Aside from alignment and balance, anything else I need to look for?

 

check for defective tie rod

 

Might want to check for brake pads also, they might have worn out.

 

worn out brake pads shouldn't cause a shudder at high speed unless you are braking.

 

also check for rim damage.

in my case, my winter rims are perfectly aligned but it is not hub centric!

 

check your wheels and make sure your wheels are on tight..

 

Typically at that MPH it is a wheel balance problem. Sometimes the weights fall off the rims, make sure weights are on. Usually a tie rod shimmies all the time until you get going faster. You should also check and make sure you don't have any radial ply separation.