When you first start the Laserfiche client, you can see the version at the lower left of the Laserfiche login window. You can also see the version by checking the "About" link typically found under the "Help" menu item.
As per your recommendation, I checked and determined all of our Laserfiche installations are currently at 9.1.1.489.
When I tried running the SP1 on my computer I ran into the above noted issue.
I re-downloaded and the SP1 from Laserfiche, re-extracted the contents, and again tried installing it on my computer with the same result.
In the end, I uninstalled Laserfiche from my computer, restarted, ran the SP1 update, rebooted, and then the SP1 (9.1.1.548) installed successfully.
For your reference, below is a screenshot of our Laserfiche Server showing the version:

Last evening I tried running the Laserfiche SP1 on the Laserfiche server, but ran into the exact same issue.
If you select "Modify", you are presented with a check mark box listing of the components you'd like to add/remove.
If you select "Repair", the update seems to run its course, but there is no change in the version. I rebooted the computer to ensure the "Repair" took effect.
I guess I'll contact our Laserfiche reseller and see if they can assist me with this issue.
Thank you,
Jason Wagenaar