Not really Hitlers mistake, but the Luftwaffe's. When a squadron of Heinkels got lost one night over Britain and bombed civilians, that was pretty much the beginning of the end.
During WW-II, Messerschmidt produced many aircraft fulfilling many military roles, including bombers. Without knowing which airframe you have in mind, there's no way to answer this question. Actually almost all Messerschmitt aircraft were designed as fighters, even the notably underpowered Me 110. Many versions of the Me 109 could carry 1 x 550 or 4 x 110 pound bombs. The Me 110 E, G and H models - could carry 4,400 pounds in various configurations. (my father has many photos of them in Libya carrying 4 -1,100 pounders.) but was very slow with this load. - The Me 210 had under fuselage racks to carry 2 x 2,200 pound bombs, but seldom did. The Me 410 could carry 2 x 2,200 internally and 4 x 110 pound bombs under the wings. - Having said all that, remember that almost all of these aircraft were in fighter units and fighter pilots do not like to be weighed down with bombs. -That was up to the Dorniers and Heinkels in their opinion !
Hienkel HE 111 bombers and Messerschmitt 109 fighters were the most common aircraft manufacturers used. The Heinkels had engines built by BMW which reverted to making cars after the war.