I've thought some more about the advantages and disadvantages of right clicking to select the method vs. typing a keyword. The click method is a faster way to test the methods, but then the worksheet doesn't show the method selected. The right click method is obscure to new users. So here is a new idea that should challenge the developers.
Add another section at the bottom of the solve block. This section would be called "method". In the section would be a field with a drop arrow. Clicking on the arrow would show the available methods for the function that has been previously entered in the solve block. Selecting one method would allow the menu to collapse and the field would show the method selected. This is like the field for US State in most online address forms.
The trick is for the available methods to be changed according to the function, e.g. find, minerr, odesolve, etc. The list of methods shown should only be those that apply to the function in the block.
With this design, the method selection procedure is obvious, not hidden as with the right click method. Also, the documentation is complete because the method name is shown. And finally, we don't have to remember the exact spelling of each method.