While typing, matching strings should be highlighted. Here is a design:

Very important thing to do, hard to see where the searched text is without this!
I would agree that search highlighting needs to be added and was about to add a request if one had not been made. There are 3rd party clients for Windows, Linux and OSX that support this feature and as much as I love the official Simplenote app this is the single reason why I am no longer able to use the official app. My notes in the application are beginning to get long and detailed enough that search highlighting is critical.
I just have to say that I stopped using the official Simplenote app just because this does not exists. It is actually quite useless when the notes are more than a few lines without search highlighting.
Another request for this in https://twitter.com/user/status/749116726701281280
there is highlighting in the android client. Puzzles me how this is not included in the windows version, I have not made the switch to the official windows client for this reason alone. Hope its included soon.
Still not added in Version 1.0.3. I am not able to move to SimpleNote because of the absence of this feature alone
Please implement this soon, hundreds of notes are not easy to navigate through without a search highlighting...
In two days from now, this request turns one year old, sad that it is still dragging. I'm speaking for the Linux version. I'm wondering what makes the task difficult if the full-text search across the notes itself is working?! Anyway, casting a vote for this being so important.
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Very important thing to do, hard to see where the searched text is without this!