Wow! This is weird. I have a 97 Pathfinder, and for the past week, I've experienced similar symptoms as you (Shimmering while accelerating the gas; Sputtering like about to run out of gas). I thought I had bought "bad" gas, so I bought (Gas treatment -STP); Didn't work. I had my gas filter replaced (Oil Change); Didn't work. I had my Dist. cap, Wires, and Plugs replaced (Tune-Up); Thought that got it, but after driving some distance, same thing.
Then I noticed that the Temperature had risen to beyond "HOT". I happen to be in close vicinity of where I had my Gas Filter replaced. I pulled in and told the mechanic what was occurring. He said, "Pop The Hood". He felt the Radiator. It was extremely HOT. He opened it, slowly and cautiously. The fluid (Coolant) was "really" LOW. He re-filled it to the top. He also said that he had a PathFinder, and the same thing happened to him when his Coolant was low. He didn't charge me for the Coolant. I drove off, and my Temperature Gauge regulated back to normal. Coincidently, my pre-existent problem had vanished (No Shimmering or Sputtering).
Soooo, what did I learn? The difference in price of Replacing Gas Filter, Dist. Cap, Wires, Plugs (Few Hundred Bucks) vs Coolant ($4, $5, in my case FREE) PRICELESS!
My consolation. Hey, the car was overdue for a Oil Change, Tune-Up, anyhow! (Now, how do I tell the wife I can't fix the Icemaker this month, because the car needed to be rapaired) She'll, say, "I guess we'll be drinking COOLANT!"
Hope this helps you.