Short attention spans are normal, just as is wanting to be moved around is normal. Like another reader, I have found slings (I recommend the Peanut Shell, Baby Bjorn, and Ergo) to be an excellent way to keep baby satisfied while I do things around the house. My little guy is most happy when I'm wearing him while vacuuming; he can even fall asleep during this particular chore. A friend of mine recommended the book, Playful Parenting by Lawrence J Cohen (on sale for $10.17 on amazon.com) that you might want to check out.
Being overly-attentive isn't harmful to your baby but it can make you feel a bit crazy when your baby doesn't seem to be responding to your efforts. Some things to try that have worked for me include:
1. photo shoots - we take photos daily and sometimes just the sight of the camera, since he knows it means mommy time, can have a calming effect
2. mini movies - I'll come up with a concept for a 30 second to 1 minute movie, shoot it, and have my baby be the star (the upside of this is that you get lots of cute footage of your baby doing ordinary things but your brain gets a workout because you've been thinking of the storyline, etc.)
3. wearing the baby - I even do this while cooking, however, when I come in contact with a hot oven or boiling water, I'll set my baby down before continuing
4. buying/borrowing mind-stimulating toys - such as activity mats, exersaucers, johnny jump-ups. I move the exersaucer in the kitchen (I like to bake) and he'll play for a while before getting very upset
5. rotating toys - pick a few and put away the rest, sometime later (a few days, a week, etc.) swap those toys for some "new" ones
6. go to the mall - window shopping can be a great way to keep baby entertained without costing a fortune
7. playing music and dancing as opposed to watching t.v. (there was a recent article published in the journal Pediatrics that suggest using educational videos under the age of 2 might do more harm than good because there is a link between high video exposure and attention problems)
Good luck. I get that fried brain feeling every now and then. I would recommend trying to get a night off, even if it only means you get an hour in a bubble bath while someone else watches your baby, to recharge.