42 aircraft is pretty paltry for a ship clocking in at 33,000 tons, even without employing a deck park. Additionally, as far as I can tell her total hangar area is similar to the Shokaku class, which were rated for 72 operational aircraft without a deck park, plus reserves. Was this some sort of weird doctrinal or operational constraint, or was there another reason for it? Additionally, did the Germans ever plan to expand her air group to a more reasonable size?
The problems with Graf Zeppelin's air group were both bureaucratic and doctrinal. One key problem was that the aircraft were not controlled or provided by the German Navy. Instead, they were owned by the German Air Force. This was largely opposed to the carrier. It was occupied with its own build-up. Diverting aircraft and resources to the carrier project would take them away from the Air Force's more pressing interests. The German aircraft industry was already struggling to meet the Air Force's needs; building significant numbers of aircraft to put on a carrier would put more pressure on it. Putting the aircraft on the carrier would also imply that the Navy had a significant amount of tactical control over them. This was generally unacceptable to the Air Force. It was strongly invested in having total control over all German aircraft and in remaining an independent service. Putting aircraft under naval control, even to a small amount, compromised this - the German Army could use this fact to argue that it should have more control over aircraft assigned to tactical support, for example. As such, it was strongly in the interests of the German Air Force to limit the numbers of aircraft the carrier operated.
The other major problem was with the concept of operations intended for Graf Zeppelin. Most navies let carrier aircraft make free take-offs, with catapult take-offs limited to more occasional operations, such as when making a full deck-load strike or when the wind over the deck was low. This was not the case for Graf Zeppelin's aircraft. They were entirely expected to take off using a catapult. In theory, this would allow the ship to launch her air group very quickly, and allowed for more control of the aircraft in the rough seas of the North Atlantic. The aircraft were placed on carriages which moved on rails on the deck. These carriages would then interface with the sleds of the compressed air catapults. This was a fast system for launching aircraft but put a hard limit on the number of aircraft the ship could operate - she could only launch as many aircraft as there were sleds available. Eight sleds (and two reserves) were provided for each of her two catapults. Carriages were more numerous, but still limited. With this concept of operations, there was no point having a large air group, as only sixteen aircraft could be launched in a single strike; it would then require a long period of loading aircraft onto sleds and recompressing the air for the catapult. It's likely that the Germans would have realised the flaws in this system with experience, but as Graf Zeppelin was never completed, they never got this experience.