I have a 2000 Ford Focus. 87 unleaded has always been an acceptable gasoline to use. For the past 8 months I have noticed more severe shaking at acceleration, whether I accelerate from a complete stop or I am already moving. I had maintenance done on time and had no change from before and after this maintenance. In a desperate attempt to "fix my car" without having to take it in, I put a higher quality 91 unleaded. My car still shakes and drags, but much less with this higher quality. Does this sound like a bad fuel filter, transmission, or something else?
The only thing which higher octane gas will solve is pinging (knocking or pre-ignition).
As an aside, just because the gas is a higher octane does not mean it's higher quality. Higher octane gas does not burn as easy as lower octane gas. At most gas stations, the higher octane will not be any better.
This does, however, differ given different brands of gasoline. In the US, there is Top Tier gasoline products which have a higher level of detergent in them. This could possibly help your situation, but it can take a some time for it to really clean things out.
Depending on your mileage, I'd highly suggest your car needs a tune up. This would include plugs, wires (if equipped - if coil on, would not be needed), and O2 sensors. This is, at a minimum, a great place to start.
After that, you'll want to clean the MAF with electronics cleaner and change the air filter. Once you've done these very simple things, run the car for a while and see how it's doing. If no improvement, you'll probably need to ask more questions here and possibly see a mechanic.
another thing to check are the engine mounts. i wouldn't be surprised if sixteen year old american rubber had degraded enough to transmit more shaking to the chassis.
You could check the sparkplugs for fault signs. Please make sure the insulator has a light brown coloring. I suspect you received the wrong types of spark plugs (heat range), producing glow ingnitions