Combination of a slightly underpowered MBA with a 1.6 GHz Penryn, a slow as hell HDD, and a heated system as soon as you close the MBA's lid/also ensure vents are open.
I would go about running a 24" LED ACD on your MBA in one way. Open the lid, run one app at a time, and understand that the HDD is an incredible bottleneck. Reduce heat by ensuring that the back of the MBA has nothing blocking the vents and maybe buy a fan to sit under it if you want to keep the lid closed. When I have seen spinning beach balls, I have always had an overheated system OR I have been seriously expecting by multiple IO tasks hitting the HDD.
I will bet you that fixing any one of those circumstances will yield better results. I was working with a friend on his 1.6 GHz MBA, with Nvidia 9400m, but it had a stock SSD, and I couldn't believe how badly it was struggling. Well, I was used to the Runcore SSD. When we were trying to move multiple files, while we had a few apps open, and we were working together, we got spinning beach balls for an hour straight. The whole system froze three times when we went to print. This was all while plugged into my 24" LED ACD. He had just over 100 GB on his SSD, and his MBA was running 18 degrees hotter than mine while I am connected to my ACD.
After an hour, we switched over to my MBA. It didn't struggle with anything. I have to believe that your situation would even be worse with an HDD vs. a stock SSD. These MBAs are nice but they're not miracle workers. In addition, the drives are a serious limitation especially in the HDD model. What we have to remember is to expect less when we're doing many tasks or when our system is driving a super HD display like the 24" LED ACD.
You could also watch the heat and activity monitor and see what apps might be causing problems. However, I would expect to see what you're seeing under those conditions. But I think you can greatly improve performance by just trying to keep the system cool, ensuring it's open and the vents aren't blocked, and by only hitting the HDD with one request at a time. That HDD is by far the biggest factor in the MBA. Remember when you tax your system with more requirements things are going to heat up.
Good luck.