There is no diode from /RESET to VCC. A (wrong) signal on the DTR could raise the voltage of the /RESET above VCC and turn it into HV programming mode and corrupt the bootloader. That is not funny. I think you should really add that diode.
The RX and TX are not protected with a resistor. It is not needed, but you could add resistors between the connector and the ATmega328P of 100Ω to 1kΩ.
The RX is open and floating, thus it is receiving noise. The signal is idle high, therefor you could add a pullup resistor between RX and VCC of 10k.
There is no capacitor between AREF and GND. I suppose your analog values don't have to be accurate. That's okay, you can almost get the same accuracy with averaging many samples.
Some usb-serial chips have 3.3V signals. The RX and TX will probably work, but a 3.3V DTR signal might not be enough to reset the chip.
I don't know which RX or TX goes to D1 or D0 of the FTDI, you have to check that with an official Arduino schematic, for example the Arduino Nano.
Where did you buy the FTDI module ? On Ebay/AliExpress/Amazon ? Then it is probably counterfeit. If something is not working properly, then throw that one away without thinking about it. Can you buy from a good seller or buy another module with other chip ?