One of the best improvements would be to place a full ground plane on one side, (often called a Pour). With a full ground plane all of your separate ground traces go away, all that is needed is a pad or a via and you have a ground. Once you eliminate all the ground traces you'll have a many ways to simplify the rest of layout, the board could likely even be made 30% or 40% smaller.
If you're not mounting the LED's and switches on the board (you don't show any silk screen shapes) it is usually better to bring most external connections to the edge of the PCB. That way you will not have wires running to the middle of the board making assembly and board mounting more difficult.
Revise the push button function to be a momentary short to ground, (detect a low signal instead of a high). That way you could make use the internal pull up resistors of the ATMEGA I/O pins. That change would eliminate the need for the five 450 ohm resistors.
If you don't required the LED connections to be on the left side: You could move the crystal downward and closer to the ATMEGA chip, then move the LED connections and associated resistors to the right side top corner of the board. Bring the LCD data connections to the right. Those changes could help reduce the board size significantly, (eliminates much of the needed space to the left of the ATMEGA chip).
Place mounting holes where needed early in the PCB design. Doing this early reduces the potential problems of having to move components or traces later that wind up being too close to screw heads or mounting bosses.
If at all possible, try not to mix SMD and through hole components on the same board, (for eg. caps on the crystal pins). If being made by an outside vendor this adds extra steps and costs. Even if being made by hand this adds difficulty and requires extra tools.
Keep trace to trace connections at 90 degrees angles or greater. Tight angle connections tend to be less reliable and sometimes do not etch well.
When making a trace connection to an IC initially try to run the trace straight away (at 90 degrees). This gives more clearance in case you need to run a new trace between the IC pins later.
As in other comments, it is best to add one or more by-pass caps on the ATMEGA power pins (VCC to GND), this should be placed as close as possible to the pins. With that said, if you are going to use a socket for the ATMEGA try to add the correct size outline around the existing chip graphic. That way you will know how close other components can be placed at the sides of the chip.
Many of the other comments have very good advice, be sure to review them all.
Best of luck with your design.