Remark out as many serial statements as you can.
With any luck you can scrape a few bytes back and it will compile and run.

Even if you have some form of debug define set for serial output the serial statements are still viable memory hogs.

Yup just change the debounce until your second trigger is no longer an issue. and well done going opto it's much safer.

That delay is only 5ms and the 1000 is 1s.
Times on delays are only approximate as the program takes time to run itself causing other slight delays.

Find out where the second pulse comes from and mitigate it.

You already have a debounce in there so increase the time there to start with.

You may also want to put a voltage divider in there too in case its actually a voltage spike as suggested already.

Is there any sort of relay involved in the whole circuit as it could also be chatter ?

Another noob here getting same error. Also not finding gateway on my specified port 5003

Have port fwd the internal IP 192.168.0.3 and reserved it in router.
Using the V3 of the ethernet shield
IDE is 1.6.5
Board is a UNO
Have a 10uF cap between GND and 3.3V