Catalyzes the dephosphorylation of different sugar phosphates including erythrose-4-phosphate (Ery4P), ribose-5-phosphate (Ribu5P), fructose-1-phosphate (Fru1P), fructose-6-phosphate (Fru6P), glucose-6-P (Glu6P), and also imidodiphosphate (Imido-di-P) and acetyl phosphate (Acetyl-P). Selectively hydrolyzes alpha-D-glucose-1-phosphate (Glu1P) and has no activity with the beta form.