Looks like to much light/heat. I may be wrong though. Just as another post had asked about a cool season plant. Well snaps are also a cool season plant.

I thought of this as I was walking away.

It also could be that if you added a fertilizer that the it burned the leaves.

If you didn't add a fertilizer then ignore this post.

It doesn't look systemic, which means from the root, so if it is the fertilizer you may have just burned the leaves and not the root, which is a good thing. Just clip the leaves off and it should be ok. And when fertilizing try to not get it on the leaves and dilute it a little more, seedlings do not need much fertilizer if any at all.

Thank you, countrycarolyn.
Light could be the culprit since I have exposed the basket to sunlight for last 4 days for about 8 hours a day. As for fertilizer I did fertilize them but I used half strength of fish emulsion fertilizer applied at the stem with a squeeze bottle, the leafs were never touched. Funny thing is that I have 8 more small pots with same snapdragons that were treated exactly same way (sunlight and fertilizer) and none has any spots at all. Not a single leave is damaged. I am thinking that maybe the soil has something to do with it. The basket has different soil.

Sometimes on a seedling they are way more sensitive than a mature plant that has been harden off in the elements. A little dab will do you when it comes to fertilizer. I have learned that the hard way. You can kill a plant fast when using fertilizer. A small drop on a sensitive seedling leaf is all it takes to burn a leaf.

Is fish emulsion fertilizer or is it form of manure? I can see leaves being burned with chemical fertilizer but decomposed fish mixture is something else, or is it. I have decided to water and fertilize from bottom only when needed. The seedlings look really strong and when I transplanted them had a good root system growing through Jiffy pot netting wall. They were actually growing into paper towel on which the pots were sitting!

It would be considered a fertilizer.

Granted some advise to fertilize when growing, but I am serious when I say this. I have had more plant failures due to over fertilizing than what I have had from under fertilizing. Once you over fertilize a plant that you love and you recognize it and do everything that you can think of to save the poor fellar and you still lose the plant, you tend to NEVER forget it. :(

This is me and only me, but I would say do not worry about fertilizing those little guys. Just talk to them and they will listen and they will start to talk to you!! :D

Problem solved after I have sprayed with horticultural spray about a week ago and they look terrific. I have posted more pictures on my blog.

Here is a link that might be useful: Seedlings updated pictures.