My Mint plant is growing very tall and it's healthy I guess by the looks of it, but I notice that the whatever-you-call-it that supports the leaves are too thin and my plant is always falling over, so I just made a small wooden supporter. It's working for now but I wonder if it is because it's not growing properly.
Plants often grow tall, spindly and "leggy" because of not enough light. The poor things are trying to climb up closer to the sun. In order to grow into the form we usually see, a mint may just need to be outdoors in the bright sunlight.
If you do have a brighter indoor spot, try moving it over there and see if it helps "fill it out". Otherwise, it seems green and healthy with the supports you have provided. It's an indoor mint; it looks good.
I agree with Lorel C. that your light levels might be to low. Remedy this by putting a LED or CFL light on it and give it a couple of extra hours of intense light if you don't have a brighter spot in the house.
For my indoor plants, I like to do two other things to strengthen them. First, with things like mint, I pinch the ends leaving 2 or 3 leaf nodes attached to the roots. That will shock the plant into putting out side shoots. Pruning mint is good for it since it responds well by producing more mint.
Also, I run an oscillating fan against my indoor garden and seedlings for an hour or so a day this strengthens the stems and makes them be able to support more plant later. I know that sounds crazy, but it works, I put it on a timer and have the breeze blow for 15 minutes at a time 2 or 5 times a day. It works miracles with tomato seedlings. Start from far away, you not doing a model shoot, just trying to get the little buggers to sway a little. And change the fan location once or twice a week.