"You retain features from your class, race or other source, and can use them if the new form is physically capable of doing so." Mobile appears to be a feature from an other source, and most forms will be physically capable of using it (if you transform into a giant barnacle, sorry...).
Would the mobile feat carry over into Wildshape? (Attacking without provoking AO)
I would say yes.
"Not all those who wander are lost"
"You retain features from your class, race or other source, and can use them if the new form is physically capable of doing so." Mobile appears to be a feature from an other source, and most forms will be physically capable of using it (if you transform into a giant barnacle, sorry...).
There are a number of threads asking what caries over when wild shaped. It is largely subjective.
I would say yes. Your DM may disagree. Just go with what your DM says.