Given the complexities of being a parent, life itself, cultural difference, etc. -- how does one begin to evaluating yourself as a parent without being bias, or getting biased feedback?
If you are asking the question, then that's all that matters. The act of asking the question implies that you care how you are doing as a parent and that means you're likely the best parent you can be already.
So don't sweat it. Enjoy the kids.
This is a hard one. First it depends on the age of the children. I sometimes ask my 8 year old what questions I should ask on this site, to see, from her point of view, what I need to work on as a parent (obviously a biased source). I read parenting books and evaluate their advice and then evaluate myself based on that. I have a friend who is a child psychologist who notices things I do right and lets me know he is impressed. I evaluate (in my head) other people's parenting and try to repeat or not repeat their behavior.
I hope that helps, really not an easy question. Remember that we all make mistakes! My husband and I joke when we make a mistake that we catch that at least we will know why our child will be in therapy. It takes the sting out of the mistake.
Do you love your children?
Do you give them your time?
Do you prioritize on their behalf?
Do you provide for them?
Do you protect them?
Do you teach them right from wrong?
Do you model for them the principles that you are teaching?
Do you teach them humility?
Do you let them fail gently and them help pick them back up?
Do you encourage them?
Are you patient?
Are you kind and gentle?
Are you consistent?
If you answer yes to most of these questions, you're doing alright.
This is a bit of a flippant answer, but it's the one I remember when I'm dealing with first-world problems:
Not the deepest sentiment in the world, but I think it makes the point memorably.
I think that it's human nature to believe that "my way is probably not all that bad" while at the same time having just a little doubt now and then.
I think it's impossible to evaluate yourself without bias, unless perhaps if you're Mahatma Gandhi or Viktor Frankl. You also can't expect a truly unbiased commentary from others, because everybody views the world through their eyes.
The best you can do, in my view, is to ask trusted friends and complete strangers (and, as Morah points out: your children!) how they perceive things and just listen without arguing. Then, later, pick from their response the parts you can use and the parts that nag you at night, and leave the rest behind.
I don't often question or review my own ability as a parent. But when I do consider my parenting skills, and when I discuss with my wife how we're doing, I most often compare to what I know best - my own upbringing. I think most of us can relate to the statement that I think my parents did a good job but there a few things I'm going to want to do differently. Curiously, I sometimes find myself doing pretty much exactly like my parents did, for better or for worse.
My best indicator of my parenting skills comes from seeing how my son interacts with other people (kids as well as adults), and secondarily how he does with us parents. I am very pleased to note that he is very well-behaved -- whatever that word means to me. To you it might have a different meaning, and that's fine; difference is good, as long as we can all still get along.
Everybody has weaknesses, and I know and acknowledge at least some of my own. Admitting them is only the first step though, and most of our traits are so deeply ingrained that we cannot completely prevent them from shaping our children. Showing awareness and effort on my own behalf helps.
I also have beliefs that are contrary to those of the culture around me, and I consciously try to minimize this friction. At the same time though, standing firm against the trend can be a strength, but it needs to be exercised with care.
You also have strengths, you have traits that make you a better parent in some respect. Allow yourself to be pleased about these, but don't count and compare them against the number or weight of your weaknesses. At the end of it all, be content to be just satisfied if you feel you're doing reasonably well.
Nobody is perfect. It probably wouldn't be fun, anyway.
I think most responses are good. I will add here a methodology to help us see clearly how we are doing.
Any evaluation requires a clear definition of a set of goals and means to measure the progress or lack of.
The first step is to make a list of "What we really want for the child". Keep on the list only what is in our reach. Keep only the most important items. It should be relatively short list (5 items?). This list will be modified as the child grows older and new needs arise.
The second step is to decide on how we will measure our progress for each item on the list. For example, "when my child learn to do something", or "when he stops doing something". Subjectively give a grade for each item. As others suggested, we can only be subjective. I believe this is good enough if the goals are defined clearly. we may solicit feedback from others who are close to us. Teachers evaluation of the child can be of great help.
Re-evaluate periodically. For low grade items, analyze the causes and adjust accordingly. You may also consult literature and professionals.
I evaluate based on what my parents did or didn't do. I tend to believe that my parents did it poorly, so that is my baseline for comparison.
I simply try to do it better than they did. Everytime I feel I did better, I chalk up a score and make a touchdown signal.
End result: my older (20,18) kids like me enuf to drop by unannounced to eat up all my lasagna, and my younger kids (10,8,6) just sat and watched "CNN Presents: Anonymous" with me.