Disable Error Reporting In Windows 10 Home

Update
As moab has pointed out, you can also disable the Error Reporting Service through services.msc. I was not able to confirm if this worked correctly myself.

Original Answer
It appears that the only option available to Home users is to disable Error Reporting via modifying the Disabled key in the registry.

Open Regedit. Navigate to:

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Windows Error Reporting

Find the value named "Disabled" or add a new DWORD value with this name if it doesn't exist. The default value of this key is 0. Double click it to edit, change the value to 1 and save.

This disables the automatic appearance of the dialogue where Windows is searching online to try to find a solution. You are instead shown a dialogue stating that the application has crashed, giving you the option to Debug. However, unlike previous versions of Windows, no error code is provided in this dialogue. The specifics of the error must be accessed through:

Control Panel\All Control Panel Items\Security and Maintenance

Under the tab "Maintenance", you can click "View reliability history", which will show a list of all app crashes. You can then click "View technical details" beside each crash to get more detailed information, such as a the error code(s) thrown from the application on crash.

Screenshots:

Debugging is still very flaky even after disabling Error Reporting. I'm not sure if this is an OS issue or an issue with the debugger(s) compatibility with the OS mechanics.

I noticed on my windows 10 (10 sep 2015) the error reporting service doesn't show up in services.msc, and the registry key is not there. However it still works and shows up as "off" in control panel > security and maintenance after I manually added the disabled key and set it to value 1.

As above, open regedit, navigate to

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Windows Error Reporting

then go to Edit > New > DWORD and name the key disabled, then change it's value to 1.