So there's not any issue with the beer dropping back to 60 after the peak metabolic time, but before the yeast 'clean up' their junk?
Actually, I came here to mention that, noting that it seemed to be ignored. Kudos for noticing when others didn't.
Most of the junk SHOULD be cleaned up, although theoretically, you may run into slight diacetyl issues. In reality though, it is very likely to be negllgible. If you're not detecting buttery/butterscotch flavors, it's nothing to worry about.
It may not end up as clean as it could be though. Most highly experienced brewers these days prefer to ramp up the temperature as fermentation continues partially because of this. You're fermenting cool enough to begin with that it probably won't be producing heaps of off-flavors in the first place, but it will likely struggle to clean them up - some byproducts/intermediates moreso than others.
Obviously, this will limit your ability to produce certain styles well. You can absolutely forget about doing a saison, which is the most obvious example. Other styles will just be difficult to produce in a balanced manner, or with the profile you may prefer (like hefeweizens).
But also, another reason why ramping up the temperature is a popular method is to promote full attenuation. Especially as fermentation slows down and it falls back to around 60°, at such a low temperature for ales, it will probably often not attenuate as fully as it otherwise could. Some strains of yeast that are particularly sudden in going from balls-out fermentation to very slow activity, like driving 100mph into a brick wall (and the resulting quicker temperature drop), could potentially make the yeast stall.
Of course, not all strains of ale yeast work optimally at the same temps, so if you continue to use no form of temp control whatsoever, look at this data on the strain before deciding to use it.
Lastly, one could expect fermentation to have slower starts at these temperatures, providing bacteria a greater chance to gain a foothold. It shouldn't be too bad, it's not really that far off from a good starting temperature for most strains if you plan to ramp up, but sanitary practices need to be very thorough - although ideally they should be no matter WHAT temperature you're fermenting at. The reason lager yeasts are pitched at double the amount of ale yeasts (ideally) is BECAUSE yeast is less active at the lower temperatures used, largely to ensure quick starts, so it follows that you could probably benefit from somewhat higher pitching rates as well, without the off-flavors typically associated with overpitching at higher temps. You may want to experiment with 25-50% higher pitching rates to see how they impact your finished product.
But really, I'd ultimately recommend some form of temperature control, even if crude. In my opinion, there have been two distinct phases in the life of my homebrewing "career", and the beers I was able to produce: before temp control, and after. The aquarium heater as people have mentiomed is a decent solution for the price, because it's more automatic due to the built in temperature controller. Brew-belts can be picked up for next to nothing, and while they are simply on or off, the position can be adjusted for finer control (lower = warmer), in addition to various methods of keeping only a portion of it in contact with the bucket. It's a really cheap solution, and largely more convenient than an aquarium heater, except for the need to monitor the temperature via a stick-on fermometer or something similar. These things can achieve much warmer temps than a lot of people realize, so if you go this route it's best to be conservative with it in terms of position (start with it high up) and contact area. Brew pads or whatever they're called, that you sit your fermenter on top of, are quite similar in terms of pros and cons, but in general I find the belts to be superior.
Kind of a longer post than I had intended, but I hope it helps. I know I mentioned a lot of cons to such a low ambient temperature, but the reality is, most of these effects are slight and probably would only be noticed by relatively seasoned craft beer drinkers, though I think it'd be really difficult to do well in competitions - or at least those judged by BJCP-certified beer judges, since many local competitions are often judged by complete amateurs - although because of this, success in such competitions often have little to do with actual quality and more to do with mass appeal anyways.