You should also note what channels have this issue and from where that channel originates. For example, if it is a problem on CBS from your local CBS station but not a problem on TNT or ESPN (which are cable or satellite only), it might come from you cable company's conversion.
Local HD channels broadcast in the ATSC digital format, while your local cable company normally will convert that to QAM digital format. These two are somewhat different and while quality conversion is very possible, you cannot tell if your local cable company is using the best conversion equipment or if the settings on that equipment are the best possible. This two can cause issues.