I have been trying to prepare rösti a number of times these last few weeks with meager results. I have tried both making fresh rösti from grated potatoes and using vacuumed ready-to-fry rösti from the supermarkert.  Grating potatoes myself took a lot of time and yielded the worst results, so I will describe my issue based on the slightly better experience I had with processed mixes (according to the package those only contain potatoes and vegetable oil).   The rösti tends to stay too fluffy, and when pressed with a spatula (tried metal, plastic, and wood) constantly sticks to it - so that I cannot compact the mixture well. The lower layer of the rösti became somewhat robust a couple of times, but trying to lift it from the pan to turn it around always broke the rösti into bits. I can't seem to find an optimal ammount of pressing the rösti together: press too much and the rösti sticks to my spatula as well as to the bottom of the pan, press it too little and it doesn't clunk together well.   I am sure at least my "sticking" problems could be diminished by more advanced kitchen utensils (not that mine are bad, but they are definitely not chef-grade ^^), still, seeing as this is a traditional dish which peasants likely prepared in iron pans, I would expect it to be comparably easy to omelettes. What am I missing? And no, oiling the pan better doesn't help, the oil just gets absorbed by the rösti and makes them fattier. 
I have finally found a solution to this issue, which, apparently, many complain about on the internet. I am specifically answering my question about frying, and this should go for both store-bought mixes and self-made ones. Based on my experience, however, I recommend store-bought.  Solution:   Do not form the rösti "pancake" (I shall call it röstitaler) immediately. Let the mix become dark yellow and sticky before you press it together. Add oil only after the previous step. It is very easy: squeeze the rösti in the corner o f a pan, spread the oil on the rest with the spatula, and then form an evenly thick röstitaler on the oiled part. Fry the röstitaler at a very low temperature (my dial goes from 1 to 10 and I have found 3 to be ideal), an old industrial thermometer says that's about 160°C (pretty much just barely the maillard temperature).  Do not try to flip the rösti like a pancake or lift it with a spatula. The röstitaler comes off remarkably easy and stays remarkably stable if, instead, you place a plate over the pan, turn it around, and then let it slide back in.   To help make sense of these recommendations, you should keep in mind that what keeps the röstitaler together is not the crust (as many would think) but the fact that dehydrated potato bits clunk together like dried cotton t-shirts. For this reason, in order to get a resilient taler, you need to make sure that most of the water evaporates before the first crust burns, but after you have actually formed the röstitaler.  