As you can see in screenshot there's a strange "stair" effect in menu labels.

P.S. Tried to disable, with chrome webtools, padding from ".ui-accordion .ui-accordion-header" css rule. The stair effect disappear but all labels are sourrounded by a white box.

I've also reinstalled simple-press plugin from scratch but it doesn't help

looks like another plugin might be loading a conflict jquery ui or library?

no way to tell from a picture though... can you look at the loaded js libraries?  what other plugins are you running that might add similar in backend?

do the links function?

as mentioned in your other post today, it seems your wp theme is loading its own version of jquery ui instead of the version that comes with wp... this is a recipe for disaster and violates wp standards... and leads to conflicts...

if you wp theme is loading its version of jquery ui in the admin, this is likely the cause... other wp plugins expect to be using the wp version of jquery ui, not some custom special loaded version... and of course, the accordion stuff uses jquery ui...

but I have no way of knowing what is loaded in your admin...