Yeah that green mush is crazy smelly. Pretty sure that's just bile. Just wash it off as soon as ya can.
BTW... if you inspect the Rabbits... (which many folks recommend you do, to see if it has Tularemia (sp?)) Don't freak out... you'll see a green looking thing on that liver underneath of it "that just don't look right". But don't fret, it's actually the gall-bladder. It looks like it could be some kinda worm thing and will weird you out.
ALSO... you're highly likely to come across Bot fly larvae when cleaning game. It'll be like inside their nasal cavity or sometimes in the ear canal or something like that. They are surprisingly large. Don't know how the poor critters can deal with havin' 'em up in there like that.
A lot of time you'll see skin-tags on the rabbits ears. That's perfectly Ok. If you don't know what they look like, Google that as well.
You're highly likely to encounter Fleas on your Rabbits. Be aware of that.
You're highly likely to find a bunch of ticks on the under-belly of the deer, nearer to their genitalia. It just is what it is. Have your gloves on, be sure to have sprayed your clothing with the permethrin spray ahead of time. Check your sleaves and pants legs often during processing. The freakin' Ticks are damn near indestructible. To kill them you're going to have to cut/crush thru their bodies with a knife blade as you find them once you get back home and are processing the meat or hide. They will survive just fine in the cooler. You will likely NOT be able to crush them between your fingers. Their exoskeletons are insanely strong.
When you manage to take a deer... and you are skinning it... take care to NOT leave those thin layers of muscle tissue connected to the hide. Those are a pain to fuss with fleshing-off when you're at home processing the hide for tanning.
Everybody and their Mama is going to tell you... when you are working with a replaceable scalpel blade knife... SLOW THE EFF DOWN!! And ALWAYS be thinking about where that knife blade is going to go the moment it cuts thru that stubborn tendon you're working on! Make sure you bring stuff with you to attend to a wound that you can cause yourself by not paying better attention to these details and you shank yourself with that scalpel blade. It happens VERY fast! Also MANY dudes have (for some reason) stabbed themselves in the thigh with them while processing big game. I've seen many videos and posts where dudes have messed around and stabbed into that Femoral artery, which is a very serious situation.
So... again.... SLOW THE EFF DOWN!!! When you finally get lucky and bag your first deer and begin to process it.
Oh... and depending on your location... possibly be prepared for the Yellow Jackets (-aka- The Meat Bees) to come and want to get all up in your kill. It will weird/freak you out the first time it happens. But it's Ok, they really don't care so much about you... they want that meat/blood. Just gently brush them out of the way with your gloved hand and you should be fine. Also.. on that same note... I learned to NOT remove the entire hide... only to remove it from the current body part I'm working to remove the meat from. For me this minimizes the problem of the Yellow Jackets coming in and getting all over everything.