Is there a dashboard widget that one can use to persistently edit a text file?
For example, suppose I want to have my
changelog open all the time in a Git repository.
It may be worth asking some of the folks at StackOverflow if you need help learning the code to accomplish this (web coding is better suited to that community), and you can use tools like Dashcode or Hype (my recommendation) to actually create your widget.
I looked at Apple's Dashboard developer documentation and it seems that widgets run in a sort of sandbox within their 'bundle', almost like iOS apps do. That would make it very difficult to implement a text editing widget.
There have been known vulnerabilities in the past, such as this one in OS X 10.4, that probably make it even more difficult now to circumvent the Dashboard 'sandbox'.
I browsed the different OS X Dashboard widgets in Apple's widget directory and there doesn't seem to be any widgets that may do what you need. Here is the developer widgets section, for instance.
There may not be a widget that does exactly what you're looking for. If there is one, it would be a great thing to know about; as I also think that having a quick notepad of sorts in the Dashboard would be quite useful. Good luck on your search.