Hi T.,
First, I do NOT have a spotless house! :) I feel your pain. We are crammed into a 2 bedroom duplex with a baby, a toddler, a cat, and a goldfish. I have a couple of ideas on ways we've tried to minimize what is all over our house, so here they are:
Our downstairs closet is now our computer office. We can shut the door on any paperwork messes, my file cabinet is in there, and when we have mail or receipts, at least they are in one place. We keep a folding chair flat up against the door when it is closed.
I have a canvas basket under a bookshelf with diapers and wipes so they are handy but not all over the place (in theory--the kids tend to toss them around the house by the end of the day).
When I know we're going to be really really busy, we use disposable cups, bowls, plates, and picnicware. We don't have a dishwasher and I hate spending more time washing dishes than playing with my kids. You can find some that are pretty "earth friendly" too.
We used to hang up all of my older boy's crafts, but now I am taking digital pictures of them and just filing away the really special ones. You could also try a large frame to have a feature picture and just rotate out with new artwork. Each of my kids has a file for stuff--pictures from Sunday school, printouts from the doctor's office, etc. My files are not professional but everything has a file. You might have to learn to toss some crafts, but if you keep pictures you can remember them better.
I have a basket in our closet/office for mail that I intend to do something with (statements not filed, subscription offers I want to use, etc.). Even though it is not tidy, everything is in one place. I also bought a mini paper shredder from Wal Mart. It is smaller than a shoebox and perfect for shredding home mail that is personal and it keeps me from forgetting what I've already sorted. I have a pretty box from a craft store that I keep all financial stuff in that is in use (a notebook where I write in monthly bills and when I pay them, statements, articles on budgeting, etc.).
I also picked up a book a while ago called "Kick the Clutter." It has some great ideas but I am sorry to say I have not acted on all of them. I photodocumented my house room by room to help me see what I want it to look like vs. what it really looks like.
I try making a game out of cleaning--what can I get done as quickly as possible (during a commercial break, while the kids nap, while the coffee is brewing, etc.). That sometimes helps get something done.
I don't know that busy moms can ever really accept that they can't keep their homes clean. I feel like my mom raised three kids and worked full time and somehow kept her house clean, but maybe I was too busy enjoying her to notice that it wasn't. You're not alone. I hope you get some great tips that I can also use!
The Addition:
You've gotten some great advice on here and I am glad you asked your question. I wanted to add that something a friend and I did before she moved out of state was trade kids on a Saturday. I took her little boy for a play day so she could tackle sorting her living room and cleaning her apartment. We also had a baby clothes sorting date. We had our kids play together while we sorted a roomful fo baby clothes. If you have a non-judgemental friend, you might be able to have a cleaning date and get some extra help. I focus better cleaning somewhere else than I do at home. The alternative might be to trade kids so you know they are having fun and getting attention while you can focus on keeping your home safe and healthy. With two little boys my biggest priorites are our health and safety (so vacuuming because of the asthma and to avoid ants, tripping hazards, etc.). Other than that, I would love it to be cleaner and more organized but not at the expense of time with my kids.