Well that post just cost me a couple of hours.

And still 136 bytes off 431:

  #define p printf 
  int main(){const char *g[]={"A Partridge in a Pear 
  Tree.\n","Two Turtle Doves, and","Three French Hens,","Four 
  Calling Birds,","Five Gold Rings,"," Geese-a-Lay"," Swans- 
  a-Swimm","t Maids-a-Milk","e Ladies Danc"," Lords-a-Leap"," 
  Pipers Pip","Twelve Drummers Drumm"};
  const char *d[{"First","Second","Third","Four","Fif","Six","Seven","Eigh","Nin","Ten","Eleven","Twelf"};for(int i=0,j;i<12;i++){p("On 
  the %s%s day of Christmas\nMy true love sent to 
  me\n",d[i],i>2?("th"):"");
  for(j=i;j>=0;j--){p("%s%s%s\n",j>4&&j<11? 
  d[j]:"",g[j],j>4?"ing,":"");}}}

You can shave 25 more by using printf as is, removing "const", removing spaces between char and *, and removing parenthesis around "th".

Are those consts really necessary? There are also a few character missing after char *d.

> Are those consts really necessary?

Technically yes, initializing a plain char * from a const char * (from array decay) is a constraint violation (an error the standard requires the compiler to detect and complain about) even in C89. Many compilers will let you off with a warning though.

which characters are missing?

"]=" after "*d["

It's not necessary in C.

   const char *d[{"First","Second",...,"Twelf"};

is not a valid C unconditionally.

You should tell my compiler.

To be honest, I understand code.golf's premise, but still, code being public (maybe optionally?) would be nice.

I agree. Stack Exchange's Code Golf has public source, but the best there is 644 bytes: https://codegolf.stackexchange.com/a/4198

Is it broken for anyone else the code prints hello world and then some numbers

The leaderboard is public but the actual code is private, that hello world is just an example c program.