Can a stereospecific / stereoselective reaction produce a racemic mixture of enantiomers? I think I have my terms mixed up but I'm confused about the concept of stereoselectivity / stereospecificity as they relate to reactions with alkenes.

For example, hydroboration is a stereospecific reaction. It leads to syn addition across an alkene. However, you can form a racemic mixture from it because you can add from either the top or bottom faces. 



I think this is a good depiction of what I mean. It seems to me that hydroboration is called stereospecific because it does syn (rather than anti and syn). But it still forms two different stereoisomers, so how can we still call it stereospecific?
You haven't mixed up your terms: a stereoselective reaction is defined as one which preferentially forms one stereoisomer over another. Likewise, all stereospecific reactions are also stereoselective, also stereospecificity has stricter criteria then plain old stereoselectivity.

However, you have to remember that the term stereoisomer encapsulates both enantiomers and diastereomers. The hydroboration reaction is stereospecific because reacting one particular diastereomer of the alkene (either cis or trans) leads to one particular diastereomer of the product. It doesn't necessarily lead to a particular enantiomer. Basically, hydroboration leads to the formation of a racemic mixture of a particular diastereomer.

The alkene you have chosen, 2-methylbut-2-ene, is not a good example substrate that can actually show how the reaction is stereospecific. Since one of the alkene carbons is symmetrically substituted, there's no diastereomerism present in the products. If we use (2­E)-3-methylpent-2-ene as an example substrate, then it becomes clearer:



Note how neither of the (2​R,3​R) or the (2​S,3​S) stereoisomers are formed. However, the two products that are formed are enantiomers of each other.