The "old" AE System?
There are a lot of things people did, that have been nerfed as the system has been in place. It's hard to give a comprehensive list since it's an ongoing back and forth.
However the most recent round of changes has to do with the proliferation of Boss Farms. A custom enemy group with either a custom critter or an existing NPC, but only the Boss rank. Then a mission would only spawn Bosses. This was changed so that a custom group needs all 3 ranks to get full xp. Additionally custom critters are modified so they need a full complement of powers to get full xp.
"Null is as much an argument "for removing the cottage rule" as the moon being round is for buying tennis shoes." -Memphis Bill
There were a number of exploits.
The first one was Comm Officers, which have minion HP, one attack and Lt rewards. An 8-man sized spawn would only spawn one portal, even if it consisted of over a dozen Comm Officers.
The second was Mending Mitochondria, which have no attacks - only a self heal. People would make an entire map of them and have no risk of being defeated.
The third was creating custom enemies with no ranged attacks, and then hover-blasting the map. Since the mobs had no ranged attacks, as long as you stayed airborne there was no way you could be damaged.
The last was boss farms, where people would make an entire map of bosses of a standard group that could be easily farmed. I think Freakshow bosses were used, since Freakshow are/were standard farming fodder.
Those were the most notable, but there are about half a dozen you missed that I heard about at one point or another.
"Null is as much an argument "for removing the cottage rule" as the moon being round is for buying tennis shoes." -Memphis Bill
total kick to the gut

This is like having Ra's Al Ghul show up at your birthday party.
Broadly, without giving everything away, here are a few general varieties I can think of.
- People created missions with foes that either could not fight back (Cimeroran Surgeons) or were not very effective foes. Sometimes these foes were also very high reward for their challenge. (Rikti Comm officers.)
- People created missions with nothing but custom foes on "Easy", which limited their attacks greatly.
- Early custom critters with melee attack sets had no ranged attacks. People filled them with melee critters and killed them with ranged fliers.
- Some critters were broken, giving heavy-duty rewards for no good reason. People filled maps with these.
- Some ally critters could be built or chosen that would massively buff the players, so they could fight other foes of choice at very low risk and/or very high speed.
- Some destroyable objects in maps could exploded and badly damaged nearby foes. However, if you did damage to the foes, you got full credit when they died, even if the object explosion killed them. People filled maps with this situation to speed rewards.
- A feature was added to let mobs scale to levels where they didn't normally exist. This broke some mobs so that they basically did nothing, but were still worth a lot of XP.
- Mobs which rezzed allies were leveraged to provide an infinite stream of foes for defeat.
- Defendable objectives spawn a massive ambush when you get near, and there was no special limit on how many of these you could have other than map size. People filled maps with these. One variant was to use large maps so you could have tons. Another variant was usually smaller maps that concentrated many of these objectives in a small area so you could maximize AoE effects on foes.
- You can build custom enemy groups that have only one rank of foe, such as all LTs or all bosses. If you can handle this sort of thing, it's very good reward per time. People mixed this with all the above variations to pack lots of them on maps. This was particularly effective if you picked a single mob that dealt damage you were good at surviving, or that just wasn't a very scary foe period. The devs decided this was too good and steeply penalized the reward for groups that did not have all three basic ranks (minion, LT and boss).
Blue
American Steele: 50 BS/Inv
Nightfall: 50 DDD
Sable Slayer: 50 DM/Rgn
Fortune's Shadow: 50 Dark/Psi
WinterStrike: 47 Ice/Dev
Quantum Well: 43 Inv/EM
Twilit Destiny: 43 MA/DA
Red
Shadowslip: 50 DDC
Final Rest: 50 MA/Rgn
Abyssal Frost: 50 Ice/Dark
Golden Ember: 50 SM/FA
I decided when I started playing that I would forgo the mission architect and just play through the "regular" missions. This has left me a little lost, though, on the AE Farms "nerf" that was implemented in issue 16. The only thing I know about AE came from the tutorial mission (and I admittedly blew thru that one). After reading the release notes I'm guessing people were creating custom mobs with standard primary/secondary powers that they could blast thru and still get good XP. Is that all it was? - seems like there had to be more to it, or, as usual, I'm missing something.