Here's some feedback
1. I found the green arrows with the amount of time required to be confusing. Where are they pointing? I'm not sure why they're on arrows.
2. You might want to use color more selectively. Make the red mean something, and the blue mean something.
3. Try to take out as much from the design as you can (as Tufte recommends). Make the boxes a light gray color, and as thin a line length as possible. If possible, make them have rounded corners so they're not quite as harsh. Take out labels that aren't necessary. Task: for example. Maybe you can even do a grid for the dates
earliest start here latest start here
earlier finish here latest finish here
Make the position mean something, and then provide a key? Just an idea.
4. I found the timeline to be a little confusing. You have them surrounded by month? It took a while to figure out...
5. When a task is completed, how is it shown? It would be helpful if the completed tasks and not-completed tasks were clearly marked, so that you could quickly scan what needs to be done, and who needs to do it.