I have looked through some articles on how to shoot in live view mode on 60D. Sometime when I try to focus on a specific point (by moving the focus rectangle on the screen to that point and press the trigger half wat), the dot will blink in red and will not take any pictures. Most articles that I found only teach you how to focus on either one of the 9 points but didn't mention anything about this issue. My guess is the camera doesn't have enough light to focus on that point (But this happens under daylight). Waht's the cause and is it possible to work around this?
Live view mode uses contrast detection to achieve focus. This means that if you try and focus on an area with low contrast, it can have trouble focusing. You can either switch to manual focusing (and zoom the LCD view to help achieve sharp focus), or move the point to an area with good contrast (ie an area with a dark area next to a light area).