R27, C16: Oscillator frequency. Arbitrary. Pick a frequency suitable for the project. Typically 100-130kHz.
R26, R28, R32, C18: Opto feedback path. C18 = 0, resistors designed for proper voltage range. The topology is wrong. Normally, you wire the internal error amplifier as gain = -1, which would be done with resistors like so:

Which leads to the next parts,
D15: omit (replace with short), add resistor across opto (pins 1-2), add R+C across IC4 ("cathode" to "adj"). This provides compensation. The supply is hopeless without the RC.
There's no aux winding. Will R29 be able to supply operating current? Normally, controller VCC is sourced from an additional winding on the transformer. This also removes any need for limiting supply or output voltage (D9-D11 can be removed completely), and significantly improves efficiency (R29 can be about 100k 1W).
R30: the UC3842 output stage can supply about 1A, so from VCC around 15V, the resistance should be about 15V/1A = 15 ohms. It can be smaller to improve speed slightly, or larger to reduce EMI.
R34 = 1V / Ipk
Ipk is determined by operating frequency, supply voltage, and output power. If Vin = 300V and P = 50W, then Iin = 0.167A DC. At 50% duty cycle, Iin = 0.333A average during the on-time. The on-time is linearly rising, so Ipk is twice this, or 0.667A. Add 20-40% more for tolerances, and you get maybe 0.8A, or 1.2 ohms.
R33 = 10k or optional.
R31, C17: typically 1k and 220pF. Time constant determined by transformer's stray capacitance and transistor's gate capacitance.
Q6 drain: needs a snubber. dV/dt preferred. C = Ipk / (2*Vin / tr). tr is the desired rise time, usually similar to the gate time constant (for IRF840, Cg ~= 6nF, and if R30 = 10 ohms, then tau = 60ns). 100pF would be typical here. The diode can be UF4007, and the resistor should give an RC time constant shorter than the minimum on-time. 10kohms would be fine.
The RC also serves as damping for the unloaded ringdown of the transformer. The RC values can also be chosen based on best damping there.
The transformer should have a primary inductance of L = Vin / (2*Ipk*Fosc), or about 2.2mH for this case.
The unloaded ringdown will be around 200pF (from Q6 Coss and reflected equivalent D12-D14 Cjo) and 2.2mH or 240kHz, which is pretty low, maybe low enough not to care. The impedance is sqrt(2.2mH / 200pF) = 3.3kohm, so the snubber R being near this value will give better damping.
A smaller transistor could also be chosen, especially a newer one with significantly reduced Ciss and Coss.
Lastly, output side: don't split grounds. You're inviting ground loop and worse EMI problems than whatever you imagine you're trying to avoid in the first place. Keep them all on common ground, and filter that ground.
With common ground, you can also jointly regulate supplies. Change R35 to 20k, and add an 80k resistor from IC4 "ADJ" to C23 (+12V, but before the LC filter). As shown, only the 5V supply is regulated, which means the 12V supply voltage will go crazy if the loads are mismatched.
Also, the LC filtering is not without scrutiny. You are making a C-L-C resonant circuit, which needs to be heavily damped, otherwise the supplies will likely be worse (due to ringing) than the noise you filter from them. The critical parameters are again R, L and C. The two capacitors (C23 and C25; C24 and C26) act in series, so have half the capacitance and twice the ESR of a single capacitor (assuming identical components). You might have 220uF and 1 ohm in this case; if the inductor itself also has an ohm or more DCR, then sqrt(220uH / 235uF) will be smaller than the total ESR+DCR, and the network will be overdamped (good).
Using less C, more L, or higher quality L and/or C (e.g., very low ESR aluminum polymer) would lead to problems. The values as shown, assuming reasonable component choice, are probably good.
Tim