Are there any other cases which indicate a denovo mutation which I missed so far?

child carries a HOM deletion, he would be './.' while parents are both '0/0' and '0/0' because they both carry a HET deletion because the caller didn't detect the HET state.

I don't think you can rely on the order of the genotype calls to identify which one is the father and the mother, i.e. I'm not even sure 1/0 can be a valid output. I would always compare with both parents and only consider:

Heterozygous de novo variant
Child = 0/1 | Mother = 0/0 | Father = 0/0

De novo homozygous variant
Child = 1/1 | Mother = 0/1 | Father = 0/0
Child = 1/1 | Mother = 0/0 | Father = 0/1

Child = 1/1 | Mother = 0/0 | Father = 0/0
This last one seems really unlikely, but I guess if you see a case like this you should count it too (or take a closer look at the genotype quality).

And by the way, it's possible that you have values other than 0/1; a . means insufficient coverage, and you can also have numbers >1 for alternative alleles. I ran a summary of the first million lines of a gVCF file and here's the summary I have:

 988916 0/0  
   6935 0/1  
     50 0/2  
      8 0/3  
   3833 1/1  
    115 1/2  
      9 1/3  
      8 2/2  
      5 2/3  
      1 3/4  
      1 4/5

Also GATK has a more formal guide on calling de novo variants, you should probably try to use something like that since it incorporates genotype quality: https://software.broadinstitute.org/gatk/documentation/article?id=11074

Step 3: Annotate possible de novo mutations
Tool used: VariantAnnotator
Using the posterior genotype probabilities, possible de novo mutations are tagged. Low confidence de novos have child GQ >= 10 and AC < 4 or AF < 0.1%, whichever is more stringent for the number of samples in the dataset. High confidence de novo sites have all trio sample GQs >= 20 with the same AC/AF criterion.