In Premiere ELements, make sure you are using the correct Project settings. If you are using a HD camcorder, use HD 1080 project settings to create your project and then you can transfer your media clips in it.
To confirm if you are using the correct project settings or not, after you put your media on the timeline, you should not see a red line above the timeline if the project settings are correct.
Looking at the specs. on the HDR-FX1, it records in 1080 MPEG-2, but the exact CODEC (Audio & Video) is not listed. The freeware utility, G-SPOT, can get all of that info, including both the Audio and Video CODEC's used. The specs. indicate that the Audio is 16bit (48KHz / 2 channels), or 12bit (32KHz / 2 channels) PCM/WAV (uncompressed) and if the 16-bit setting was used, it should not be an issue. However, sometimes those spec. sheets can be wrong, or an update to a camera model might change things. G-Spot will tell you.
If your camera is set to the 12-bit Audio, change that to 16-bit. The 12-bit setting is just for adding narration through the camera, and that is better done in your NLE program.
Also you can try by switching off the "Enable GPU Playback" option in Edit>Preferences>General.