For starters, the good news is the design is clean and fairly easy to read.
• As a designer you need to hold your ground. Adding a flickering star animation will only cheapen the logo. Ask them for a reference to any other well known logo that features an animation to their logo on their website.
• If anything the current logo needs to be cleaned up. The design and images used on the site are crisp and clean. Yet, the Mustang Group Holdings logo is blurry, muddy, using too many gradients in the images and text and DOESN'T need a drop shadow. I would do the mustang in a solid color (blue or black) and again a solid color on the name. NO DROP SHADOW.
• Why the difference in the main image/quick links/our brands? I would think a larger image that shuffles through that showcases all would work better. Also don't like how you have two sections of shuffling images. Too much is going on. One section featuring shuffling images should be plenty.
• It seems like a pretty small website. If that's the case I don't think you'll need a search box.
Hope that helps.