When watching a video with the built-in media player, the video volume sometimes is quite low, even when set to maximum. Using the same headphones, music is loud enough though. Is there a possibility to increase the volume for video playback? If it's not possible using built-in settings/apps, maybe there is an alternative video app with a volume overdrive setting?
The volume of audio and video played on your phone depends on the volume of the file itself (see technical details here). For example, you might play a video on YouTube and then a similar video on Vimeo with different maximum volumes.
Having said that, it is not impossible that there may be a problem with your phone speaker. Test this out by transferring a music file from your PC to your phone. Play it on maximum volume- if it seems reasonable, then you know that the phone speakers are not at fault.
Finally, there are no apps on the marketplace that allow you to boost or normalize volume. However, since you are on Windows Phone 8, you might see some improvements in updates that will soon be available.