Project Server 2013 error: Faulting application name: schedengine.exe

As me moved to Project Server 2013, I have made several posts along the way describing new bugs introduced in the Project Server 2013.

Here is the one that I see pretty regularly:
Can't save or published the project. It's been queued and never finished.
The event log registered an application error:

Faulting application name: schedengine.exe, version: 15.0.4551.1507, time stamp: 0x52700711
Faulting module name: schedengine.exe, version: 15.0.4551.1507, time stamp: 0x52700711
Exception code: 0xc0000005
Fault offset: 0x000000000048508b
Faulting process id: 0x1e68
Faulting application start time: 0x01cf3eca3fc01ef1
Faulting application path: C:\Program Files\Microsoft Office Servers\15.0\Bin\schedengine.exe
Faulting module path: C:\Program Files\Microsoft Office Servers\15.0\Bin\schedengine.exe
Report Id: 6a2866f8-aad9-11e3-9414-00155d52365a
Faulting package full name: 
Faulting package-relative application ID: 

This bug is not a new one based on the reply in this thread
In my experience, the common cause of such behavior is wrong dates for task duration.
What I mean by that is the following:
As an example, you have a Task 1 with duration 1 d and dates are: start date: 3/12/2014 and finish date: 3/13/2014. It's 2 working days based on the dates.
That situation is never been reproduced intentionally, but I saw it after the fact. So, I don't know how to reproduced, but it's obvious how to fix it.
You need to open the project in Project Professional and recalculate dates (F9).
In some cases, it might be the other issues related to some wrong data that appeared in the project, that schedengine can't get it straight (which is a whole another discussion)
As a recent example, when I checked the dates and nothing was suspicious about them, I have tried to publish the project through Project Professional, which is really helpful since you have a error message more easily than scanning through event and trace logs. So I have got a Job UI that failed and search by it in the ULS log messages field and found the following error:
Cannot insert duplicate key in object 'pub.MSP_PROJECT_RESOURCES'. 

I have checked the resource values that are not currently in the resource list and select the actual one, saved and published the project successfully.

This is a known bug and acknowledged by MS

I have ran the recommended sql to fix the issue. That ensures that we will not have this issue from now on.

Nevertheless, the inflected projects ARE NOT FIXED AND NEEDED MANUAL ADJUSTMENT.

Almost every project is affected. 

To fix the remain residue:

1.      open the project in the Project Professional ;

2.      re-add missing resource;

3.      re-select the resource in the tasks that shown with numbers instead of resource name

4.      Save and Publish