Q. “What problems (if any) arise when the iron is oxidised?”
A. Haemoglobin will be converted to methaemoglobin which cannot bind oxygen.
To quote from the article on Methaemoglobin in Wikipedia:
Methemoglobin (English: methaemoglobin) (pronounced "met-hemoglobin") is a form of the oxygen-carrying metalloprotein hemoglobin, in which the iron in the heme group is in the Fe3+ (ferric) state, not the Fe2+ (ferrous) of normal hemoglobin. Methemoglobin cannot bind oxygen, unlike oxyhemoglobin. It is bluish chocolate-brown in color. In human blood a trace amount of methemoglobin is normally produced spontaneously, but when present in excess the blood becomes abnormally dark bluish brown. The NADH-dependent enzyme methemoglobin reductase (diaphorase I) is responsible for converting methemoglobin back to hemoglobin.
The question also asks:
“…the higher the oxidation state of the cation, the higher its
polarising power… hence stronger the bond.So wouldn't
iron in the Ferric state be able to bind with oxygen better…”
which can be transformed into:
“Why can‘t methaemoglobin bind oxygen?”
The answer is chemically rather complex, but one thing you should be aware of is that in haemoglobin (and myoglobin) the oxygen Fe(II) is five-coordinated (as shown in the diagram below where Fe is black) and binds oxygen in the sixth position (to the right).
In simple terms, the electronic change in oxidation to Fe(III) causes a change in the geometry of the haem pocket such that oxygen no longer can bind (although now water can). This page elaborates the point, without providing a full chemical answer.
Footnote: Fe(II) or Fe2+ ?
Some readers may be wondering why I have referred to the ferrous state of Fe in haem as Fe(II) and not Fe2+ (which the Wikipedia entry uses). This is to avoid implying that there is an overall charge of 2+ on haem groups in haemglobin and myoglobin. Inspection of the structure of haem (above) will show that the formation of two covalent bonds to imidazole nitrogens has left haem with a zero net charge.