As a leader how open are you to constructive criticism when you are approached professionally?

If you are not COMPLETELY open to hearing what someone else has to say, you are not a good leader. If you want to be a GREAT leader, you will ASK for other opinions and accept any and all criticism.

the main word is "constructive". :)

The key is that constructive criticism needs to be given in a respectful manner. Too often as leaders we provide counseling statements to our subordinates, and give them criticism as a means to fulfill a requirement. Does constructive criticism need to be given? Yes, but it needs to be done in a way that will not only be understood, but in a positive and respectful manner to contribute to growth. We should never approach it as "this is what you need to work on" or "this is what's wrong with you". It should be approach like "you've been doing an amazing job, but there are a few things you can work on to outshine your peers and grow as a professional," "some of my observations were a, b,and c, I'd be happy to sit down with you and discuss my observations and work with you to develop a plan; I really think working on these areas would improve your performance and help you in future assignments". Try to keep it positive, and also highlight what they did well.

Sorry about the long example, but basically I'm saying it needs to be a respectful conversation (give and take) with attention paid to their body cues. If they do not look like they are open to constructive criticism at that time, it may be better to approach it later or ask someone who has a better relationship with the individual to provide the constructive criticism.