4 way switch

http://www.automanualparts.com/wiring-diagram-for-3-way-switch-with-dimmer/

use above link

Connect the green dimmer wire to your ground wire

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Add a comment with clear description of each wire and what Load is being controlled.
Why are you using a 4-way switch? Are you controlling 240Volt circuit?

Photoelectric switch usually has red, black, white wires, and usually replaces a single pole switch but can also be used to control 240Volt circuit in some wiring diagrams.
http://waterheatertimer.org/images/Wire-photo-eye-125.jpg

4-way switch has 4 screw terminals and is generally not used to replace a single-pole photoelectric eye, but can be used to control 240Volt circuit in some wiring diagrams, so I'm not sure what you are doing.
http://waterheatertimer.org/images/Typical-3-Way-switches-450.jpg

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Your screw terminals are 2-brass and 1-dark.
Dark screw is considered 'common'
http://waterheatertimer.org/ST01C-program.html#3-way

Leviton shows a 3-way 1203-2, but not 1201
Wiring diagram indicates that pilot light is ON whenever switch has power.
http://www.leviton.com/OA_HTML/ibeCCtpItmDspRte.jsp?item=2681§ion=10046&minisite=10026

Check your instruction sheet that pilot light is supposed to turn on-off with Load.
I don't think it is, without additional terminal on switch for neutral wire.
And then it would only work on switch located closest to light.

You can wire this type of thing separately.
Buy ordinary pilot light or indicator light from WW Grainger.
Look at diagram on following image:
http://waterheatertimer.org/images/3-way-circuit-with-pilot-indicator.jpg

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Review old switches:
Two old switches > each has 2 wires
Old switch 1 > Red and White
Old switch 2 > Black and White
The same white wire connects to both switches, so effectively they count as 1 wire
This means you have 3 wires ... 1 White, 1 Red, 1 Black
Each switch controls a separate load (light, fan, motor)

New Leviton double-rocker switch:
-Leviton has 2 Brass-colored screws on one side, and these screws are connected together by a brass plate >> your Hot wire will connect to brass screw
-Leviton has 2 Silver-colored screws on other side, and neither of these screws are connected in any way >> the wires going to each load will connect on a different screw on this side of switch.

Hot wire: Each box in your house has exactly 1 hot wire that is connected back to breaker box. This is true for all boxes (excluding boxes that have a 3-way & 4-way switches).
We need to identify Hot wire.

-By code the Hot wire is black for identification purposes ... but your box sounds like maybe the Hot wire is White.
-If your Hot wire is white, that is NOT an immediate safety issue ... it will not cause a fire or malfunction ... it is a code violation ... because code requires things be uniform so next electrician knows what previous guy did. So some day, electrician working outside grabs wrong color wire, and wow. I say this so you know.

Moving on.

Identify Hot wire:
-Pull 3 wires up so they can be tested
-Turn on power
-Use ordinary tester, or old lamp with plug cut off and wires stripped back
-Tape tester lead to sticks so hands are away from voltage
-Power is on. Don't stand in water or touch metal pipes, and you're fine.
-You have 3 wires in box + ground wire
-Test all 3 wires to bare ground wire >> when tester lights up, that is Hot wire ... testing is complete

Connect wires to Leviton double-rocker:
-Power is OFF.
-You have 3 wires - 1 White, 1 Black, 1 Red >> one is Hot wire, the other two wires go to load
-Hot wire connects to Brass-colored screws on new Leviton.
-Brass colored screws are connected together by a brass plate so the Hot does not need to connect to both brass screws.
-The other two wires connect to Silver screws on other side of new Leviton switch
-One wire goes to each silver screw
-Connect bare ground wire to green screw.
-Push wires back into box. Use eraser end of pencil if needed.
-Make sure ground wire is back and away from screws on switch
-That's it.

Switch has 2 black wires. One black is hot wire. One black is wire going to fan. Turn off power. Remove wires from switch and separate. Turn power back on. Using ordinary tester, test each black wire to bare copper ground wire. Only one of the black wires will test hot. The other black wire goes to fan.
Timer black wire connects to black hot
Timer blue wire connects to black wire going to fan
Timer white wire connects to white neutral (in absence of white neutral, connect Timer white wire to bare ground)
Timer green connects to bare ground wire

remove white switch one and connect to incoming white ground--all whites should be connected [hooked] together these are grounds-- switch 1 black from fan ,leave switch 2 red from fan ,switch 3 vanity black

I assume you have 2 of the three way switches and this 4 way is between them. Do you have a non-contact voltage tester? They are a great investment for less than $15. Do you also have some way to test continuity? A cheap voltmeter or just a flashlight bulb, battery, and a little wire? If this presents no obstacle, then do the following--- remove the 4-way switch and spread apart the ends of the 4 wires as much as possible. Have somebody stand guard over these wires for safety (and maybe put a wire nut on each of them) then turn on the power. Only one wire of these 4 will be "hot". Take note of which wire this is. Now flip both of your 3-way switches. (If you know which of them is the "upstream" switch, you only need to flip that one.) Now, a different wire of the 4 will be "hot". You have now identified your 2 "In" wires. Turn off the power. Before connecting your switch you need to test it's continuity. You are looking for a pair of terminals that have no continuity in either position of the switch. (there are two such pairs, either pair will do). Connect the two wires you identified as "in" to the pair of terminals you just found. (either wire to either terminal, it doesn't matter) Connect the other two wires to the other two terminals (either wire to either terminal, it doesn't matter). You are done. If it still doesn't work, you have a problem with one of the 3-way switches.

You have two of your carrier wires from the three way to the four way switch on the wrong posts. Study the diagram to help explain where you went wrong. You can change the wires around by guessing thru trial and error. The attached diagram will help explain what you are trying to accomplish. If you know which posts connect when the switch is thrown you could figure it out, but trial and error may be the best bet. As long as you don't have a neutral wire in the mix on the switches, you won't hurt anything as long as the power is off while switching so you don't hurt yourself.

The blue wire is the switched hot wire coming from the leviton.
So:
black hot/source to black leviton -- blue leviton to black for light fixture or black "line" on GFI -- all whites connected together.

Charlie

P.S. If the GFI is only powering a light fixture, it is not needed.