Deprecation warning in Moment.js - Not in a recognized ISO format

use moment in your function like this

 moment(new Date(date)).format('MM/DD/YYYY')

Check out all their awesome documentation!

Here is where they discuss the Warning Message.

String + Format

Warning: Browser support for parsing strings is inconsistent. Because there is no specification on which formats should be supported, what works in some browsers will not work in other browsers.

For consistent results parsing anything other than ISO 8601 strings, you should use String + Format.

moment("12-25-1995", "MM-DD-YYYY");

String + Formats (multiple formats)

If you have more than one format, check out their String + Formats (with an 's').

If you don't know the exact format of an input string, but know it could be one of many, you can use an array of formats.

moment("12-25-1995", ["MM-DD-YYYY", "YYYY-MM-DD"]);

Please checkout the documentation for anything more specific.

Timezone

Checkout Parsing in Zone, the equivalent documentation for timezones.

The moment.tz constructor takes all the same arguments as the moment constructor, but uses the last argument as a time zone identifier.

var b = moment.tz("May 12th 2014 8PM", "MMM Do YYYY hA", "America/Toronto");

EDIT

//...
var dateFormat = "YYYY-M-D H:m"; //<-------- This part will get rid of the warning.
var aus1_s, aus2_s, aus3_s, aus4_s, aus5_s, aus6_s, aus6_e;
if ($("#custom1 :selected").val() == "AU" ) {
    var region = 'Australia/Sydney';

    aus1_s = moment.tz('2016-9-26 19:30', dateFormat, region);              
    aus2_s = moment.tz('2016-10-2 19:30', dateFormat, region);              
    aus3_s = moment.tz('2016-10-9 19:30', dateFormat, region);                  
    aus4_s = moment.tz('2016-10-16 19:30', dateFormat, region);                 
    aus5_s = moment.tz('2016-10-23 19:30', dateFormat, region);
    aus6_s = moment.tz('2016-10-30 19:30', dateFormat, region);
    aus6_e = moment.tz('2016-11-5 19:30', dateFormat, region);
} else if ($("#custom1 :selected").val() == "NZ" ) {
    var region = 'Pacific/Auckland';

    aus1_s =  moment.tz('2016-9-28 20:30', dateFormat, region);
    aus2_s =  moment.tz('2016-10-4 20:30', dateFormat, region);
    aus3_s =  moment.tz('2016-10-11 20:30', dateFormat, region);
    aus4_s =  moment.tz('2016-10-18 20:30', dateFormat, region);
    aus5_s =  moment.tz('2016-10-25 20:30', dateFormat, region);
    aus6_s =  moment.tz('2016-11-2 20:30', dateFormat, region);
    aus6_e =  moment.tz('2016-11-9 20:30', dateFormat, region);
}
//...

Doing this works for me:

moment(new Date("27/04/2016")).format