And I also agree, there should be a Bothan. As a primary character. Bothans were almost definitely used to recover the original DS plans (unless they hadn't joined the Alliance yet). Bothans are used for spy work because they're insanely good at it.
If they really are genetically predisposed to intelligence work, why would any sane Imperial officer not just shoot any Bothan on sight given how xenophobic the leadership of the Empire was anyway?
I just remembered that in Return of the Jedi Mon Mothma says that the Bothan spies gave them the *location* of the Death Star and information such as the fact that the Emperor was going to be there. They also had some technical information about the Death Star but unlike when they got the plans for the first Death Star they didn't necessarily need precise classified blueprints: because the second Death Star was still under construction they could just fly through the incomplete structure and blow up the main power plant. Given the enormous scale of the construction of a Death Star, its entirely possible this more general technical information was a lot easier to get than the plans necessary in ANH to locate the vulnerable exhaust port. The hard part was locating its construction site and getting information on the Emperor becoming involved in the project directly. Given that the nature of the information they got in ANH and in RoTJ was different, it is entirely possible that the Bothans would have been good at the kind of strategic information gathering that could discover things like where the empire was hiding its new Death Star and where the Emperor might be traveling, but not be as good at directly infiltrating the location hosing the classified (original) Death Star plans.
Incidentally, I think the complaints about the exhaust port on the first Death Star are overwrought. It doesn't seem to be a particularly stupid design error to me: if the Death Star needs exhaust ports at all in the first place, it might be extremely difficult to make them both impossible to attack and still properly functional. They took the precaution of shielding them from above so you couldn't just shoot them straight on. The trenches might exist specifically *because* the shielding meant the plasma exhaust couldn't go straight up and thus had to be directed outward through those trenches. They had to be long and straight to prevent problems with high volume venting. And in the pre-nuclear age warships had the same design "error" of having stacks that pointed straight up and could use used to detonate explosives bypassing the armor of the ship. It almost never happened because the odds of such a hit by a dive bomber are extremely unlikely, but it has happened. There was just nothing practical you could do to prevent it from happening.
There were probably lots of exhaust ports all over the Death Star, and in most of them the combination of defenses and their design placement made an attack on them impossible. This one port managed to be in just the right place with just the right configuration to make the attack possible but the design engineers simply failed to account for it. It was obvious enough after the attack began that an imperial officer figured it out during the attack. But that sounds exactly like the sort of error that happens in real life, both in civilian engineering and in military weapon systems.