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Date parse month format

While creating/testing a date adapter in my Angular project I ran into this issue. I think I must be missing some convention, but when changing the month to a single digit like 2 (for February) rather than 02, I get a different day.
Date.parse is giving two different outputs based on that different as pictured below. Any thoughts?

According to the documentation:
The ECMAScript specification states: If the String does not conform to the standard format the function may fall back to any implementation–specific heuristics or implementation–specific parsing algorithm.
Here, the second string does not match the expected format, and Chrome does something with it.
If you test it with Firefox, the same date is returned, so it's a Chrome "issue".
You can try to read V8's source code to understand why you get this and how it is actually implemented.
This isn't a lot of help, but I don't think you'll find anything without getting to the bottom of V8.

Moment dates are parsed different in Mozilla and Chrome?

I have an issue with dates in Mozilla, I am using fullcalendar plugin for angularJs in my project. While using the moment dates, Chrome seems to be working fine but Mozilla seems breaking. I am using Timezones with the moment. Many blogs and posts seems to mention the format of moment dates while having cross browser issues.
Here it is,
console.log(moment(new Date('2017-02-28T18:30:00')).format('dddd-MMM DD,YYYY'));
Mozilla : Tuesday-Feb 28,2017
Chrome : Wednesday-Mar 01,2017
I am really stuck with this, and I have seen post about mentioning the format with the moment dates, but I have used the format in the above sample but it fails to return the desired output. On the other hand Chrome is returning the correct result, what am I doing wrong ?
If you need any details please leave a comment.

Do not use moment(new Date('2017-02-28T18:30:00')) use moment(String) instead (since your input is in ISO 8601 format).
As moment parsing docs says:
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.
Here a working sample:
console.log(moment('2017-02-28T18:30:00').format('dddd-MMM DD,YYYY'));
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.17.1/moment.min.js"></script>
If your input is UTC use moment.utc:
moment.utc('2017-02-28T18:30:00')
If your input is in a given timezone (e.g. Asia/Calcutta) use moment.tz(..., String);
moment.tz('2017-02-28T18:30:00', 'Asia/Calcutta')
By default moment parses string in local time, you need to know timezone of your input. Note the moment has local(), utc(), and tz(String) methods to change timezone of a moment object.

You are converting a JS Date to a MomentJS date so I can only assume Firefox parses the JS date differently.
With MomentJS you should be able to simply replace your code:
moment(new Date('2017-02-28T18:30:00')).format('dddd-MMM DD,YYYY')
with:
moment('2017-02-28T18:30:00').format('dddd-MMM DD,YYYY')
https://momentjs.com/docs/#/parsing/

if you use angularjs, it's easier to use filter.
$filter('date')('2017-02-28T18:30:00', "dd/MM/yyyy");

IE 11 issue with JavaScript toLocaleDateString() formatting

I am using the JavaScript Date function toLocaleDateString() to format my date to look like 8/13/2014, but for some reason when I try to send this value via an API call by doing a JSON.stringify and then AJAXing the value, IE decides to change the actual value to be ?8?/?30?/?2014.. This obviously causes errors on the back end.
Why does IE do this and how can I fix it?

Looks like it's a bug that was introduced in IE 11. IE 11 uses Unicode chars, so what you see is U+200E 'LEFT-TO-RIGHT MARK'
What you can do as a temporary solution to fix this issue is to replace that char. Like this:
console.log((new Date()).toLocaleDateString().replace(/\u200E/g, ''));

You should check out the answer here:
ToLocaleDateString() changes in IE11
You shouldn't be using a function intended to format something for locale-specific human display and expect the output to be machine parsable. Any of the output of toLocaleString, toLocaleDateString, or toLocaleTimeString are meant for human-readable display only. (As Bergi clarified in comments, toString is also meant for human display, but ECMA §15.9.4.2 says it should round-trip)
Although the function returns a string, it's only human-readable and is never appropriate for machine parsing. I'm not 100% sure what encoding it is for IE, but although it looks like a string, underneath it uses a different encoding.
For date formatting, you may wish to use Moment.js, or just write your own formatting function.

Unexpected behaviour of javascript timestamp

I use phoneGap Geo-location API to get current position in which i got time-stamp also.
alert(data[0].timestamp);
alert(new Date(data[0].timestamp).getTime());
where data[0].timestamp = "2013-12-03T19:09:58.859Z"
in web browser the second alert shows 1386097798859 whereas when i built and test app in mobile then it alert as NaN
I don't understand why it happens?

It's a ISODate format. Try to use Date.parse or use momentjs javascript library which can parse a lot of date formats.
Also there is a gist with Date.parse polifyll.

Javascript - Retrieve OS Date formatting

Hmmm... Okay so I've been searching the web for 2 days now without any luck. I've seen a lot of answers on how to format a javascript date for example new Date().toString("yyyy-MM-dd")... Which would return something like 2013-04-05.
This is absolutely not the problem.
What I want, is the possibility to set the format in which my OS displays dates, then retrieve that specific format and display it in the browser.
For example, let's say I changed the format of the date in my OS to MM-yyyy/dd (this is for arguement sakes, whether that would work or not is irrelevant)). Then I'd expect to see 04-2013/05 in my OS, right? Next I want to retrieve this specific format in my browser via Javascript so that I can use this to format my dates throughout my webpage.
If this is lunacy and cannot be done, please tell me, as I've got a headache from searching.
Also, if you say use someDateObject.toLocaleDateString() without explaining exactly why .toLocaleDateString would work, I'm going to ignore it, because I've tried setting my date-format in my OS to numerous formats and every single time I use .toLocaleDateString(), I receive the same format: dd/MM/yyyy

first attribute of .toLocaleDateString method locale(s) used.
current locale you can obtain through navigator.language (in firefox or chrome) parameter.
in IE you can obtain navigator.browserLanguage or navigator.systemLanguage
in browsers other than IE it is impossible to obtain system language this way
after this you can call new Date.toLocaleString(navigator.language||navigator.browserLanguage) and it will be formated correctly depending on browser language