(1) Background: We made a comprehensive evaluation of executive functions (EFs) and attention processes in a group of adolescents and young adults with mild intellectual disability (ID). (2) Methods: 27 adolescents and young adults (14 females and 13 males) with ID, aged between 15.1 and 23 years (M = 17.4; SD = 2.04), were compared to a control group free of cognitive problems and individually matched for gender and age. (3) Results: As for EFs, individuals with ID were severely impaired on all subtests of the Behavioral Assessment of Dysexecutive Syndrome (BADS) battery. However, we also found appreciable individual differences, with eight individuals (approximately 30%) scoring within normal limits. On the attention tests, individuals with ID were not generally slower but presented specific deficits only on some attention tests (i.e., Choice Reaction Times, Color Naming and Color–Word Interference, and Shifting of Attention for Verbal and for Visual Targets).The role of a global factor (i.e., cognitive speed) was modest in contributing to the group differences; i.e., when present, group differences were selectively associated with specific task manipulations, not global differences in cognitive speed. (4) Conclusions: The study confirmed large group differences in EFs; deficits in attentional processing were more specific and occurred primarily in tasks taxing the selective dimension of attention, with performance on intensive tasks almost entirely spared.