mjmessina, Radio Shack has a good inexpensive sound level meter for audio testing, and combine it with the Stereophile Test CD2 for testing between 20Hz-20kHz. You are looking for a match between speakers as well as absolute output level. A driver on one side almost always goes bad first, and right to left comparison confirms that. Switching amp cables right to left checks for amp problems, or substitute another pair of speakers. Swipe some rosin flux from a flux pen on the speaker terminals before soldering, and use high strength 96/4 tin/silver solder or similar (97/3 tin/copper solder works well also) which guarantees a joint that sees vibration will never fracture. This appies more to guitar amp wiring than audiophile speaker wiring, but it can be a problem if you are pounding the driver hard.
Also, MAKE SURE that a tweeter diaphragm is firmly screwed to the magnet assembly. My DTR-25E tweeters had VERY loose diaphragm attachment screws right from my RM-1 kit arrival. Also, and this applies to your older speakers, many plastics deform under screw pressure and may need occasional snugging-up. I once purchased a pair of JMLab speakers that were sounding a bit rough, and there were loose screws all through the speaker that the previous owner never tightened down. In a few minutes with a screwdriver, I had them sounding like new. It's a good idea to flow some high strength silver solder onto all solder joints of old speakers. Substandard solder joints are a fact of life, even on something "premium" like my Rickenbacker bass where internal solder joints were very amateurish. Get a temperature controlled soldering iron and become proficient in soldering. Bad solder joints and dirty connectors are a major cause of "roughness" in sound gear.
Get some Caig DeOxit while you're at it and start using that as well, if you don't already use it. Especially useful if you're in an industrial pollution/high humidity/saltwater coastal situation. Small signal tube pins in amplifiers will need routine cleaning and application, as well as all interconnect points.
If your signal goes a bit rough but not really bad, say from high end quality to mid-fi quality, then it's probably bad contacts and/or failing tubes. An original Ei tube went rough in my C-J EV-1 after only 500 hours and caused a problem similar to yours. An expensive replacement NOS GE 6072 went bad even sooner. In certain preamp tubes, up to 75% failure rates are common even among premium American NOS tubes. 3 out of 4 NOS RCA 6C4 tubes I sent to Andy Bowman of Vintage Tube Services for evaluation were substandard for audio right from the start, and the 4th barely passed as a line stage buffer tube. All eight Mullard M8080 (military grade 6C4 equivalent) passed with flying colors and are rated 10,000 hours (but will probably last at least twice that long). My tube tester can only test for emission, shorts, and cathode performance. Only a high gain amplifier, premium output transducer, and trained ears can test for audio quality in tubes. Tubes are often microphonic at extremely narrow frequency bands and it takes a continuous sweep generator to spot them. Andy has all that stuff, and I mainly buy tubes from him these days. Most tube dealers really do not have proper audio testing equipment and expertise. Among the big volume dealers, Watford Valves from England has sent me good tubes. Stay away from Angela Instruments. A VERY high gain combo guitar amp is a useful tube tester, as the first input stage and the fact it has a speaker shaking the tube makes microphinic tubes easy to spot. You can use a slide to pick any frequency in the guitar/bass range. If a tube passes high-gain combo amp testing, then it is very unlikely to be microphonic in audiophile gear, and a small used combo amp can be had for very little money. I have a Marshall AVT20 that I paid $175 for used in good shape. The first position is a 12AX7, which can test several tube types such as 5751, 6072, etc. Everything else is solid state and eliminates other tubes clouding the results. Most of my NOS American tubes cannot pass muster in this amp.