I'm having all the same problems you have. First tried one with a new thug MM where keeping the pets under control was very hard. I had to keep them on passive the entire time and send them to attack certain things individually. If I didn't do passive they would constantly attack everything but the guards or longbow.
Then there is my 40 plant dom which was so frustrating I gave up and quit. Being only on Vicious (3rd setting) I found taking out the PPD was fairly easy and blowing things up quite the same. Then I went to the jail where a big boss and his friends awaited me but luckily had domination up and confused him to kill his friends in 1 shot each. Broke out the villain who became much like my flytrap, useless. When you can't stick them on passive they just run around beating on civilians. Finally got the NPC villain to join me in the bank (not sure how) where continued to beat on a stuck civilian in the corner while the HERO! turned up to kill me in 2 hits. I stupidly went back to try again where I found the NPC still beating on the civilian and died again in about another 3 seconds when hero saw me. Thank goodness it was only on test server.
Almost forgot about one of my major pet peaves in the mission, use of the "tab" key. I'm very accustomed to using it to switch my target but in the Mayhem mission I NEVER get the next guard, it's always the nearby barrel or civilian. Many times i would even get switched to a civilian that was 2 blocks down the street. To get a target you must always try and select it with your mouse. Not sure how to fix that problem though.