Over Generation
X-bar theory can produce sentences that are NOT well formed; It over-generates (generates ungrammatical sentences).
Because X-Bar theory says complements are optional we end up with verbs not having the correct number of arguments. e.g:
*The philosopher loves
*The philosopher smiled the breadbox.
Fixes: Selectional Restrictions
Selectional Restrictions limit the semantic properties of arguments
e.g.
#My toothbrush loves raisins.
#The bolt of lightening killed the rock
Fixes: Theta Roles and Thematic Relations
Theta Roles and Thematic Relations limit the sentences that are valid in the Grammar - they prune off the overgenerated X-Bar sentences.
Ordering of Grammar Generation
X-bar → Theta Criterion → Expl. Insertion → EPP & Binding conditions → Judgments.
Undergeneration
Word orders that X-Bar Theory can't derive (VSO, VadvO, V Neg O) are generated by head to head movement.