I had an opportunity to spend a bit of time with this recently, which might have tempered my previously negative view towards its sound quality...as my profile shows, I'm pretty familiar with the limitations of entry-level polysynths, which can either be embraced or escaped, depending on your perspective.
The minilogue's 2-/4-pole filter is pretty good, though it does not compensate for resonance level, which in some cases might end up a bit noisy when the resonance is 50% or so (as a lot of my patches are) due to the reduced noise floor. Double-saw or double-PWM patches are punchy with a bit of extra grit on the top end; for some, this might be all you need to know.
The VCOs open up a lot of possibilities as far as cross- and ring-modulation; the sawtooth wave is also sweepable by shape, though this precludes a traditional VCO1 saw + VCO2 PWM square patch as the PWM is global across both oscillators.
The envelopes do click (thump) a bit, which can be addressed with judicious use of the post-VCA HPF; similarly, as the LFO does not offer a sine wave as an option, there remains a fair bit of thump at both extremes when using a triangle wave as the modulator (by comparison, the Prophet '08 / Tetra / Mopho's triangle wave does not create nearly as audible an artifact).
And while it's nice to have a built-in delay, the problem lies with the fact that it's not sweepable (as with the Evolver / Prophet-12 / Pro-2), which is itself a missed trick. It would also be nice to see another LFO, or two, or three (env re-triggering). As others have pointed out, it has a propensity toward being a bit noisy.
The waveform display (I hesitate to call it an oscilloscope, as the timebase changes freely) can be switched off in favor of a parameter view (very handy when editing patches), or simple program-number-only view.
All in all, it's probably an excellent piece for someone who probably hasn't laid hands on an analogue synth in a while, though for those of us that might own a better-specified analogue unit (DCOs or otherwise), the limitations in modulation routing might be crippling-or not, if you like a challenge (or feel like soaking it in reverb further down the signal chain).
And I think that the minilogue's analogue voice itself would make, with better noise floor, more extensive modulation and control capabilities, an excellent-sounding synth voice as part of a larger device. It's just not all there yet, though I found myself lusting after a twin-layer, eight-or-more-voice unit with some patches.
I did not spend any time with the arpeggiator (seemed a bit wonky, compared to the better implementations I've seen) or the sequencer....