• Minecraft Version: 1.10.2
• BetterFps Version: BetterFps-1.4.3-1.10.jar
• Forge/LiteLoader Version (if any): Forge 12.18.3.2254
• Other Mods (if any):
  Mantle-1.10.2-1.1.5.jar
  TConstruct-1.10.2-2.6.3.jar

Place an item rack or a drying rack in the world. Right click it with an item. The item doesn't show on the rack.
This bug was not present in BetterFps 1.3.2.
Config (all options are on "vanilla" setting):

{"algorithm":"vanilla","updateChecker":false,"preallocateMemory":true,"fog":true,"beaconBeam":true,"fastHopper":false,"fastBeacon":false,"fastSearch":false,"asyncSearch":false}

Works fine for me. How are you installing BetterFps? There is something really wrong with your setup

Just putting the jar into "mods" folder. Is this correct?

Yes, it should've worked... I'll try to think what can be causing it.

I apologise. This is no bug. I should have tested TC separately. This is me being inattentive and misunderstanding one of TC's options.