Sticky finger problem
The atoms of the manipulators "fingers" "adhere" to the atoms that are being moved and vice versa. Advanced forms of mechanosynthesis does not work with tiny tweezers that grip atoms. It's more like playing around with direction dependent (technical term anisotropic) attraction forces.
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The "problem"
One might worry that due to that stickiness one cannot deposit enough kinds of structures to make anything useful. But as it turns out that this is not the case (see papers linked from the mechanosynthesis page). In contrary without that sticking force (noble gas atoms show that behavior at room temperature) assembling anything would be impossible.
Obviously as long as one can go down to increasingly stronger attraction forces one can let go of the cargo atom(s) (that is deposit it). (more accurately as long as the appropriate thermodynamic potential goes down) But what if one ends up at "rock bottom"?
The three tip "trick"
There are several strategies. The most obvious one is to introduce further tips. Just as one can get double sided sticky tape off ones fingers by using more area at the target site this same method works for atoms. Another possibility is to use the dependence of bond strength on (relative) bond direction (turning two tips towards each other or apart from each other) or the possibility to turn pi-bonds out of alignment.
This way one can can pump some new energy into the system (originating from the diamondoid nanomachinery in the background - force times motion distance) going back up the hill closing the loop. (The system as a whole of course still moves down a thermodynamic potential. Otherwise it would not move forward.)
No need for tremendous capabilities
Of course not every structure allowed by physical law will be mechanosyntesizable. Actually by far not.
But that is not a problem. A core principle of atomically precise manufacturing is that one can make almost anything by synthesizing almost nothing via the "magic" of metamaterials. That is via emulation of material properties at the scale of crystolecules and microcomponents. Not via the choice of different materials like we do today.
