I used to be a cable guy...er cable person.
The fact you have poor quality on televisions and intermittent internet more than likely has less to do with the quality of the splitters and more to do with the number of them. Poor quality splitters can have adverse effects if they have problems passing certain frequencies. Most worth their salt will identify the frequencies they pass. For cable TV and data I would seek out those that can handle 5Mhz (data upstream) to 900Mhz (high-def digital and data downstream).
By design, a modern cable plant should deliver the same level of signal to your home as every other home in that system. As a rule of thumb, this level can be split three to four times before you will notice degradation issues. It's when people cross this threshold that amplifiers become necessary.
Also a possible cause to your problem is the quality of the fittings and coaxial in your home. The benchmark standard today is RG6 dual or tri-shield. Older homes may use smaller diameter RG59 and long-runs (almost always service line only) will use the larger diameter RG11.
As far as fittings go, compression fittings are the best followed by crimp in and finally screw on. I would not use the latter unless there is literally no other option. Loose fittings can allow ingress (airwave transmissions reaching inside the coax and interfering with its frequencies) which could cause problems; most commonly "ghosting" or "dual image" on analog TV sets. Also, poor fittings can cause the cable to "suck out" from the fitting; creating a large gap between the end of the coax itself and the splitter/device.
Lastly concerning your internet. Cable modems must transmit back to the first node in the system at a predetermined signal strength. The level the modem must transmit to achieve this is called the return level. When the modem returns, it must transmit all the way back through the system; including splitters and loss (also called attenuation) from cable length. If the return rate is too high (over 50dBmv) you stand a good chance of experiencing intermittent service or no service at all. Keeping your modem isolated off the first split is the best way to prevent this.
Service line -> 2-way splitter -> modem (leg 1) -> other splitters (leg 2)
EDIT: I forgot. Your problems may result from a damaged service line. In the warmer months, squirrels or "tree rats" like to chew on the coax and will happily remove the shielding for you. If this is the case you will need to call your provider. Most good ones make service line repairs and replacements at no cost to you.
As a cable person I replaced a good amount of splitters but more often than not it was either a layout problem, poor fittings, or damaged cable.
Edited by MNiceGuy - 12/25/08 at 2:05am