Yes it may just be a remarkable coincidence, but these are interesting.
rs1364405
Trait: sense of direction 23andMe
G
Human copy from one of your parents
A
Neanderthal copy from your other parent
Each copy of a A is associated with having a worse sense of direction
Your DNA portal
Discover the Neanderthal markers that may influence your health
Abnormal movement
Marker (SNP): rs17813377
Genes: FRS2,YEATS4
Your number of Neanderthal Alleles: 2
Agorophobia, social phobia, and panic disorder
Marker (SNP): rs2885932
Genes: NONE
Your number of Neanderthal Alleles: 1
Anxiety, phobic and dissociative disorders
Marker (SNP): rs12486167
Genes: RAB5A,PP2D1
Your number of Neanderthal Alleles: 1
Strabismus and other disorders of binocular eye movements
Marker (SNP): rs579046
Genes: CCT2,FRS2
Your number of Neanderthal Alleles: 2
Schizophrenia
Marker (SNP): rs7652000
Genes: SUCLG2,KBTBD8
Your number of Neanderthal Alleles: 1
All things that apply to me.