Are you are planting in spring? Zone 4? If its too cold, and seeds sit too long in wet soil, they may be rotting. I find that it's easier to grow good carrots in fall anyway. Germination is quick, temperatures are more stable, and less rain to mess things up. They grow for longer, get bigger, and best of all, the late season cold makes them taste extra sweet. Spring carrots are annoying - weeds, weather, and by the time they're almost ready they get hit with a heatwave and lose their taste.
Other than that here are my techniques:
Timing - DO NOT trust the days to harvest on the seed packet. It's going to take longer. Maybe way longer. Start as early as possible in spring, or like 90-120 days before the fall frost
Seed selection - Try "Bolero" carrot seeds - They are normal Nantes type carrots, but the seeds are literally almost twice as big as a normal carrot seed, and they seem to grow way faster, stronger, and bigger than any type I've tried. They will bust right through obstacles that will mess up other carrot types. It is a hybrid, though - no seed saving.
Bed prep - Dig deep and flip the soil over with a shovel all around the bed before planting. If the soil is too dense, Add leaf compost or sand on top first. This is really where 90% of the work in growing carrots should go. The result is big, easy to use carrots.
Planting - Scoop out a hand-sized trench, fill it with leaf compost or potting mix, and plant in that. You can, for example, fill it some, sprinkle a line of seeds, and add the last another half inch on top.
I do this, not just for better germination, but because of weeds. Doing it this way prevents any weeds from coming up around the carrots. If you add some kind of weed block between trenches, you have no weeding to do at all.
Never let the soil dry out especially around germination time, and up to few weeks after. They'll be traumatized for life.
Thinning - Remember to thin to 1.5 inches. Crowding causes stress. I don't use scissors but you have to be careful about disturbing roots.
Mulch - Cardboard, paper, straw etc between the carrot rows have a quadruple benefit - weed supression, temperature stability, maintaining soil moisture, and preventing greening of carrot tops if they poke out. EZ straw (chopped straw from home depot) can be added earlier than regular straw, when the plants are very small. Regular straw can be added a bit later. You can combine these with paper underneath to really snuff weeds.
