TLDR: Don't freaking do it with regex!
The time part:
/(?:[01]\d|2[0-3]):[0-5]\d/
A basic attempt at the date part:
/(?:0[1-9]|1[0-2])\/(?:0[1-9]|[12]\d|3[01])\/\d{4,}/
A more advanced attempt at the date part (validates correctly, except for February):
/(?:(?:0[13578]|1[02])\/(?:0[1-9]|[12]\d|3[01])|(?:0[2469]|11)\/(?:0[1-9]|[12]\d|30))\/\d{4,}/
Going further, assuming each year is a leap one:
/(?:(?:0[13578]|1[02])\/(?:0[1-9]|[12]\d|3[01])|(?:0[469]|11)\/(?:0[1-9]|[12]\d|30)|02\/(?:0[1-9]|[12]\d))\/\d{4,}/
Divisibility by 4:
/\d*(?:[13579][26]|[02468][048])(?!\d)/
Not divisible by 100 or divisible by 400:
/\d*(?:(?!\d{2}00)|(?=(?:[13579][26]|[02468][048])00))\d{4}(?!\d)/
Is leap year:
/\d*(?:(?:(?!\d{2}00)(?=\d{2}(?:[13579][26]|[02468][048])))|(?=(?:[13579][26]|[02468][048])00))\d{4}(?!\d)/
Only valid February dates:
/02\/(?:0[1-9]|1\d|2[0-8]|29(?=\/\d*(?:(?:(?!\d{2}00)(?=\d{2}(?:[13579][26]|[02468][048])))|(?=(?:[13579][26]|[02468][048])00))\d{4}(?!\d)))\/\d{4,}/
A valid date:
/(?:(?:0[13578]|1[02])\/(?:0[1-9]|[12]\d|3[01])|(?:0[469]|11)\/(?:0[1-9]|[12]\d|30)|02\/(?:0[1-9]|1\d|2[0-8]|29(?=\/\d*(?:(?:(?!\d{2}00)(?=\d{2}(?:[13579][26]|[02468][048])))|(?=(?:[13579][26]|[02468][048])00))\d{4}(?!\d))))\/\d{4,}/
Now everything in one place!
Date and time:
/^(?:(?:0[13578]|1[02])\/(?:0[1-9]|[12]\d|3[01])|(?:0[469]|11)\/(?:0[1-9]|[12]\d|30)|02\/(?:0[1-9]|1\d|2[0-8]|29(?=\/\d*(?:(?:(?!\d{2}00)(?=\d{2}(?:[13579][26]|[02468][048])))|(?=(?:[13579][26]|[02468][048])00))\d{4}(?!\d))))\/\d{4,} (?:[01]\d|2[0-3]):[0-5]\d$/
Can this be simplified? Most definitely!
Will I do it? Hell no!
I think the message is clear - don't do it!