Kenmore clothes washer possibly staining clothes with grease

[gesinc]

Hello,
This is a Kenmore clothes washer m/n 110.92273100 s/n CD0907123. The wife thinks that the washer is 'spitting' grease or oil onto their clothes.  I've seen the spots and they do look like grease. The husband thinks that the spots are caused from the clothes getting caught in the front seal of the dryer. There is some side to side movement with the dryer drum but not much.
I think that it is the washer but what would be causing it, if this guess it correct.
Also, she is saying that it doesn't extract all the water from the clothes in the spin cycle.
What is starting to fail, that would effect the efficiency of the spin cycle?
I appreciate your responses.
GESINC

[Repair-man]

If there is a sign of grease, I usually pull the spin basket and have a look at the outer tub. If it is all gunked up with residue, this will show up as grease. So will a buildup of fabric softener in the agitator cap.  Poor water extraction is spin could result from a clogged pump or a worn drive clutch. If the machine does not spin properly it will not release the fabric softener.

The dryer should not have gaps in either the front or real seal. If so new rollers are needed.

Have a closer look at the washer...this he-said, she-said stuff doesn't help get to the problem

[gesinc]

Thanks for the direction. I'll check those things out. 
Definitely, marriage counseling is not my forte.