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Right now I am designing a circuit that will charge a Li-ion battery via USB, using the MCP73831 (at 100 mA).
The battery voltage (nominally 3.7 V) will be regulated to 3.3 V to power a microcontroller like an ATtiny85 or ESP8266 for example.
Below is what I have so far. My question is: Are there any flaws/mistakes I made, and how can I charge the Li-ion battery while simultaneously powering the MCU?
Because right now I can only charge OR use the MCU, depending on the SPDT switch.
Most Li-ion chargers don't charge a Li-ion battery with a load attached correctly, because the load current interferes with the charging algorithm.
Charger ICs that can support a load while still charging correctly exist, but your MCP73831 isn't one of them. The MCP73871 is; it supports load sharing and can supply a load while charging the battery.
You could add a load sharing circuit to your MCP73831 if you want to get rid of the switch; see MCP73831 Li ion battery charger problem with load sharing circuit for an example of how to go about it. There's also a Microchip application note that describes how to do it.
The problem with charging and using a Li-ion battery at the same time is that end of charge is not properly detected. The MCP73831 uses the current level at the end of the constant voltage stage for charge termination.
