I had the same problem for awhile, until I found a rough workaround - there is a free program called "Afloat" that allows you to pin the sidebar so that it is always on top of the browser window. There are some problems with using it (the sidebar will cover other app windows, for example, and will need to be minimized), but it's been a good band-aid in my experience, at least until Sidewise allows you to focus the sidebar (and not row) on hover. I think that might be difficult to implement. 

http://infinite-labs.net/afloat/#download

I am still experiencing problems (version 2013.4.18.1). I still get zombie tabs that are visible if I refresh the sidewise panel, and am still experiencing stray tabs in the chrome tab bar. Not sure if my case is idiosyncratic or not.

A related bug - for some reason when I use cmd+T to open a new tab while sidewise is in focus, "t" ends up in the search bar.

Apparently several such programs exist... the best one so far: http://infinite-labs.net/afloat/#download

I realized after posting this suggestion that the author had already planned on including this feature, but ran into some difficulties. If anyone else is having a similar problem as I am, I have found a somewhat workable solution called MightyMouse:

http://www.atomicbird.com/about/mac-apps

Enable auto-raise on mouse hover in order to achieve focus on mouse hover. Unfortunately this works for all open applications, so to restrict the feature to just Chrome, you must whitelist every other application. Messy solution, but it works for now.

This is a known bug - apparently it is due to V26 of Chrome. There is an earlier thread about it (http://sidewise.userecho.com/topic/161643-new-tab-bug/) that might give you some more information. It seems that Joel is aware of the bug and is working on it.

As far as my experiences go: the glitch is most nefarious when creating a new tab and starting a google search, but the frustrating thing is that I haven't found a way to consistently trigger the condition. With that said, it definitely happens often: if I don't pay attention, I can rack up 10+ zombie tabs in a half an hour. It just started happening a few days ago, but I haven't installed any new extensions in the meantime (Adblock, Sidewise, StumbleUpon). I will continue to try and find a reliable trigger for the problem.

I also have this problem. It creates a weird kind of "zombie" tab in its place if you remove it from the sidebar. If you press ctrl (or cmd) + R while the tab bar is focused, you will see all of those removed tabs. If you kill them and refresh again they come back. The only way I've found how to kill them for good is to hibernate, wake, and then kill them.

Shot in the dark, but given that you can't remove the top tabs, is there a way to get sidewise to show up in presentation mode?