Broadcast beds

I grow most of my veggie in raised beds.  Each bed is it's own polyculture.  I have never been one to plant all tomatoes in this bed, and all zucchini in that.  Each bed has a little bit of everything, or as of this year a lot of everything.  I have found mass planting reduces weeds, I use less water, but still had amazing production.  
Now I'm planting my fall garden. Living in N. California zone 9 b means now is the time to plant veggies that don't like the heat.  Most of the fall veggies are tiny little seeds. I just don't have the patience for them. So for the little seeds I just broadcast them in the beds, and added a layer of compost one top and called it good.  I'm sure people who like things neat and organized would be horrified.  I'm excited. It will be fun to see what comes up where.  The only thing I plant in neat rows are veggies that grow up the trellis, and my onions and garlic.  I poked spinach and pansies in randomly, so it won't look uniform for long.
I'm curious how you all plant tiny seeds like carrots?

I scrape a row with the edge of the hoe or rake or even a stick whatever is to hand and then dribble them in with my fingers. They are in rows and all in one bed as they have to be covered or the carrot root flies will ruin the lot.

I have been letting my chickens out in the evenings when I am outside.  Tonight I let them out, not realizing I left my garden gate open.  I'm so glad I didn't spend a lot of time planting.  Who knows what will still come up, and where.  I will just wait a couple of weeks and reseed in the bare spots.  They weren't in there long, but they sure enjoyed themselves while it lasted.

I've done both broadcast seeding like you describe and planting in rows. I really like the broadcast approach because it's fun watching everything emerge and identifying the seedlings. But, managing a mix of plants that grow at various rates and into various sizes was a challenge. (But, that was also fun. ;-) )  This year I planted my late summer spinach, lettuce, and chard all separately because of expected variability in overwintering hardiness, aiming to use lettuce first such that garlic I planted among the lettuce can take over next spring, spinach will last longer into fall, and I hope to overwinter the chard. We'll see!

I planted chard for the first time this spring. It is still going strong, so it will be interesting to see how long it lasts.  I thought about starting some new chard, but we already have enough for us, family, and the chickens.  So I decided to hold off.
I will plant lettuce too. I'm just waiting. My lettuce is always so bitter no one wants to eat it.  I read not to plant it until the temperature doesn't go above 80 degrees.  I'm going to try that and see if it helps.  Happy planting.

I have been getting the pelleted carrot seeds (from Johnny's) lately.  You pay a little more, but I find there is much less waste and I don't have to thin them later.  

Once I learn how to identify or distinguish the plants I can eat from the ones I can't I'll be happier to do broadcast sowing.

As it is I can only identify most of the things I planted because they crop up evenly in the rows or bunches I planted them in.

I'm starting to be able to identify brassica sprouts pretty early. Carrots I can usually tell, but there are some similar wild parsley plants here that look similar. Beets I can tell. I've got some volunteers though that I'm waiting until they are fully mature and flowering before I can identify them.

It's the same problem I have with self seeding annuals. Identification is hard.

When broadcasting tiny seeds, I first shake them up in a jar with a bunch of soil/sand/compost. It's much easier to sprinkle a cup of seed-saturated dirt evenly over the surface of a planting area than a half-teaspoon of plain seeds (and if your jar medium is different than your planting medium, you can see what you've already covered). I find that this works pretty well for seed mixes, too -- the corn/beans/whatever don't settle to the bottom of the mix as readily.

(glad to see someone else growing over the winter in california 9b! there really ought to be a PSA letting people around here know that october-march is a prime growing season, lol. it took me a couple seasons to figure out that leafy greens and brassicas do NOT enjoy being planted after last frost here...)