Embed Plus addresses that problem and others. Embed Plus allows you to start a video at any point you specify. You can also use Embed Plus to skip scenes in a video, play it in slow motion, zoom into an area of a video, and annotate a video.
The annotation feature of Embed Plus is a nice complement to the real-time reactions feature offered by Embed Plus. Real-time reactions pulls in Twitter and YouTube comments about your chosen video. The annotation feature lets you comment on specific parts of a video. Your annotations can include links that you insert.
Here's a video without using Embed Plus.
Here's the same video using Embed Plus.
Applications for Education
If you're in the habit of embedding videos into your blog or website for students to watch, Embed Plus could be a good tool for you. You can use Embed Plus to have your embedded videos start and end at the places you want so that you can direct students' attention to the most important parts. You can use the annotate with links feature to direct students to information that will build upon what students watched in your embedded video.