Check with your local DNR and Co-operative Extension Service.

To reduce the mosquito population, use Mosquito Dunks, including in the sodden grassy areas.

Adding a few water hungry trees and shrubs like Willow can help as can building up the area around the pond. Dredging can help. It sounds like the water flow is spreading out and slowing down the exchange of oxygen depleted water for fresh.

What your situation represents is the effects of siltation. The original pond has probably filled in with sediment. This may be due partly to a decrease in rainfall rates in your area over the years that precluded any strong water surges into your pond to help keep the siltation to a minimum.
There are several ways of approaching the matter.
The first should be to get an idea on the rate of flow of the water into and out of your pond or bog area.
Then determine if the outflow area can be steepened and perhaps lowered to help increase water flow out of the wet area. Then I would dredge out the pond area proper.
You may want to look upstream at the inflow system to determine if natural flow is being blocked. If it is your property then you can remove debris in the upstream portion to help increase flow into your pond. Once all this is accomplished I would let the system return to whatever balance in inflow/outflow will occur.
Do not plant any trees or any plants until the system's balance is determined so that you can have an easier stab at making whatever adjustments in flow rates you may wish to pursue, either increase or decrease. Once you have stabilized the pond water flow rate and are satisfied, then let the system sit as is for a year and see what Mother Nature will do as far as introducing plants into the system.
For mosquito control you may want to use the dunks and once the pond has cleared maybe even start working out a natural tier of fish, from herbivores to a few predatory fish, and slowly introduce into the pool, PROVIDED that plant life has returned to the pool. If not then check out what native aquatic plants are in your region and see if you can either buy or collect some to introduce into your pond BEFORE introducing fish. You should wait a year for the plant growth to reach a stage where it can be grazed without being overgrazed, or supplement with fish food as necessary.
It is a precise balancing act and may take some time to get all the vectors working in such a way as to eliminate it becoming much of a burden to your time and resources.
you may want to check with your local library on earthen ponds. I could not find a website that wasn't trying to sell either a product or a service in regards to your question.
Main thing is TO THINK IT THROUGH COMPLETELY BEFORE YOU STICK THAT SHOVEL INTO THE PROJECT! Good luck.

Thank you, Terrestrial Man!

This is great feedback. We explored "upstream" a bit and found a fallen tree that appears to be blocking inflow and causing the bog as water flows around the tree. It is on our property (or close enough, if it isn't, it's on town land and they don't care) so we're going to remove the debris and see if we can get both the inflow and outflow streams flowing cleanly.

We found some fish living in the pond already (plus a TON of frogs) so I agree that we should wait to see what happens once we've fixed the inflow/outflow issue. Your advice to wait makes a ton of sense.

I have a 3/4 acre farm pond that had issues. Found a local company that works on ponds, and they came with heavy equipment and dug out the pond.

It was wonderful for many years until this year, now I have a muddy pond which I'm wondering if that's caused by too many fish. That's another topic....

Pamghatten,
muddy ponds may be caused by fish mucking up the bottom silt but lack of appropriate aeration or water movement through or within the pond can be a major contributor to the problem. Also lack of a sufficient covering of water plants can also be a factor.
Zetts Fish Farm offers something called a gallon of water purifying bacteria which may help clear up your pond. Check their website and click on the Catalolg, then Complete Catalog link and scan to bottom of catalog.
If the pond is one that has all the run off flowing into it and nothing out of it then your problem may not be easily resolved unless the slopes leading into your pond are covered by vegetation. Just look over your situation and try to see just what is happening.

thanks terrestrial man ... looked more this weekend as the dogs were swimming ... pond is more greenish than muddy.

My pond has never had water movement and has been clear, I think it was sooo hot this summer, it probably has something to do with not enough plant coverage. I'll look at Zetts for ideas.