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I'm trying to reproduce GaAs bandgap using HSE functional in VASP 5.2. Currently I get bandgap of only ~0.6 eV, much lower than Dr. Kresse and co-authors reported in their paper. My INCAR and KPOINTS files are given below. I've tested both spin-polarized and no-spin cases with no improvement. I also tried to remove ENCUTFOCK=0 and NKRED=2 with no improvement. I use PAW PP's from old VASP distribution (VASP 4.6). I start with preconverged WAVECAR from previous PBE run. GaAs lattice constant was optimized with PBE (a=5.764675 A) Please let me know about possible errors in my approach. Thank you.

INCAR File
-----------

# SYSTEM NAME
SYSTEM = GaAs PARAM

# OUTPUT AND START
NWRITE=2
ISTART=1

# ELECTRONIC CONVERGENCE
NELM=400
ISMEAR=0
SIGMA=0.2
EDIFF=1E-6
PREC=Medium
ALGO=Damped
TIME=0.4

#HSE
LHFCALC=.TRUE.
HFSCREEN=0.2
ENCUTFOCK=0
NKRED=2

# TYPE OF RUN
IBRION=-1
NSW=0

# SPIN AND FUNCTIONAL
ISPIN=1
GGA=PE


#LDOS

LORBIT=10
NEDOS=2000
EMIN=-30.0
EMAX=30.0


KPOINTS File
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Automatic mesh
0 ! number of k-points = 0 ->automatic generation scheme
M !
16 16 16 ! subdivisions N_1, N_2 and N_3 along recipr. l. vectors
0. 0. 0. ! optional shift of the mesh (s_1, s_2, s_3)

I obtained a GaAs band gap around 0.95 eV when I did HSE06 with VASP 5.15. I can see two things that *might* help your calculation.
1) Check the OUTCAR file for significant partial occupancies. If they are there, reduce SIGMA. I used SIGMA = 0.5
2) Use an odd number of KPOINTS to get a point at Gamma where the band gap is.
I use Accurate accuracy and have ENCUT = 272, but I would think these would have a large effect. Also, I have ISTART = 0, which seems to work for me and saves a lot of time. I am using a very similar lattice constant a=1.746.
If the paper you are referring to is J. Chem. Phys. 124, 154709 (2006), then I believe the calculation that they were doing was not the same as what is done by VASP now when setting HFSCREEN=0.2. The reason I think this is that this paper was written just before Heyd et al. (the people who invented HSE) published an erratum that changed some parameters!
At least, that's what I'm attributing *my* 0.3 eV shortfall to.