Do hot circuit breakers indicate a problem?
It is never common for any breaker to get extremely warm. Residential plug-in breakers are rated for 70C. So your measurement of 125F then it is at 52C and I am guessing you're just measuring the breaker and not opening the panel and checking the lugs. If your breaker is heating up over 158F you have already done damage to to your breaker or bus. 

Breakers heat up for a number of reasons:


Loose connections - kill the power and check all connections make sure they are clean and tight at the breaker and the dryer plug.
Splices in the feeder - Check and make sure your feed is continuous from the breaker to the dryer if there are splices that are a transition and cannot be replaced see above.
Undersized wire - This may be because of voltage drop because of circuit length Not much to say except change out the wire.
Damaged breaker - I am pretty sure you have already damaged the breaker so you should just replace it as SOP.
Damaged bus in the panelboard - pull the breaker and make sure the bus is not discolored or there is arcing damage. If there is replace the panel. 


One other thing, you didn't mention the age of the mobile home. Many of the older models were installed with Aluminum conductors. If this is so you may need to No-ox the connections or pigtail the trailer.

If all of this is too much for a DIY, you might need to get a professional on site.

Remember "there are old electricians and bold electricians but there are never any old, bold electricians" so kill any panel or circuit before performing any maintenance on the electrical system. 

Hope this helps and be safe.