That can happen if Windows does not support the pound sign -- for example, if it is set up for Eastern Europe -- and if Notes' Unicode display is turned off.
In Notes, choose File - Preferences... - User Preferences... and in the list of Additional settings ensure that "Enable Unicode display" is checked. If you change the setting, close Notes and restart it to make the setting work.
Your text editor is probably hard coded to work in a US code page, ignoring all your settings. Your web browser works in the code page of the web site, and also supports Unicode.
Be careful that you do not type or paste the character L-stroke (Ł). Some fonts might display this as a pound sign, but it is a different character. If you type pound in a text editor and paste it back into Notes, you might find it becomes L-stroke. In Notes the compose sequence Alt-F1 L- or Alt-F1 L= always types a pound sign. Check that your keyboard pound sign is the same character.