I'd say that it's much more likely that you will get too much Omega-6 (Arachidonic Acid) which is a precursor to prostaglandins that lead to water retention, inflammation (arthritis) and sticky platelets. This is truly the main problem with the American diet. We get too much Omega-6 and little to almost no Omega 3. That is why supplementing it is so vital. Try to keep your intakes to the point where your ratio of Omega-6:Omega-3 is the natural level of 4:1 or 3:1.
There are good saturated fats, especially the ones with MCT's (Medium Chain Triglycerides) which actually provide energy, boost metabolism and are absorbed quickly by the body to be quickly converted to energy.
Here's the first thing you have to do though - cut out completely any usage of Trans-fatty acids. Fortunately, this fact is becoming more well-known. Anything that is hydrogenated or partially-hydrogenated. Get rid of them, they inhibit androgenic process in the body and actually lead to health problems because of their negative effects on cellular chemistry.
Also, lower usage of or completely cut out any and all usage of vegetable oils. They are very high in Omega-6 and have little to no Omega-3.
A big problem with vegetable oils is that they are extracted at high heats, which causes them to go rancid easily and they are full of free-radicals. Free radicals attack the body's cells causing oxidative damage that leads to pre-mature aging, cancer, high-cholesterol and other problems.