McClane already has practical weapons at his disposal, in the form of a repossessed sub-machinegun and his trusty Beretta. His ability to improvise weapons is largely untested. In the film he does manage to fabricate a bomb out of an office chair, a monitor, an elevator shaft and a big bag of C4. Although this is technically improvised, making a bomb out of plastic explosives doesn't exactly require MacGyver levels of genius.
None. In fact, McClane is already surrounded by enemies. Europeans are shiftless and untrustworthy, with deceitful accents and tiny little feet. Worse yet, if the Europeans decide to join forces with the zombies, an outcome we believe to be probable, McClane will really have the deck stacked against him.
The Nakatomi building is large, taking up an entire city block. Multiple entrances and exits make it hard to defend, and a rat's nest of elevator shafts and service passages allow multiple avenues for zombie penetration. A group of survivors working together could potentially hold an entire floor but, as we've said before, the prospect of anyone cooperating with Europeans stretches the limits of plausibility too far.