There are some circuits containing relatively high feedback impedances, which must be high, because otherwise they would introduce errors. As a rule of thumb in these designs feedback resistors must be about 1000 times higher than biggest shunt resistor to provide an error of less than 0.1%. If you assume a shunt of 500Ohm, then feedback resistors in the MOhm range are needed. Such a design would heavily suffer from input bias current of any bipolar OPamp. Only a FET-OPamp can be used then.

TL034 has the advantage of showing very low offset voltage typically. In the datasheet you can see relatively high maximum offset voltage data, though, but if you take a handful of these chips the very most will show very low values. Such a behaviour cannot be expected when using TL084! So, if a TL084 shall be used, then additional offset nulling circuitry might be needed, or at least a selecting by hand must be done to find chips showing very low offset voltage.

TL034 is a modern variant of TL084, where an advanced input circuitry will guarantee a much better performance referring to input offset voltage. TL034 offers an input offset voltage being four times lower than TL084.

To the watchdog: I would always use MAX1232, or similar, if possible.

Kai