If the maps don't load for players then it is one of two things: the server that nickjer uses to host the maps could be down, or the more likely the players is using a poor internet connection, two variables that TW are not able to control. Personally I would rather have the page load itself up and then load each map individually, rather than having the page take forever to load as it is trying to load 8 maps at once (2,668,688 pixels of colour).
I had first hand experience of this at my flat last year when I first moved in, I only had a 2mb connection with at least 550 students on the same network. Until a lot of them left at midnight to go clubbing it would take up to 15 minutes to load a single page, so it took quite a while to load even a basic structured web page. Web pages full of images (that is web pages made up of images, and then including more images such as the map threads on the TW forums, not forgetting all the coding that has to load to run and display the page correctly) took far longer to load, and the pages on TW only loaded quicker when images were placed in spoilers. Granted I then forked out £160 to upgrade to an 8mb connection, but even then peak times were slow
In short if the page will load quicker so we can then see the specific maps we want then that is the best way to go, instead of waiting ages for all the maps to load.
As for your problem of opening spoilers on a smartphone, I do not have a way of being able to check that myself, but as it does not appear a wide spread issue then I don't know of a sure fire way to help you there. Maybe try clicking around the spoiler button in order to find the clickable link for it?