1. When a layer is Filtered and then Selected in the Attribute Table, if you close it in the table it stays selected. Only way is to reopen it and remove the filter. Too easy to forget to do that, end users will have an issue with this. First, the layer's name in the layerlist should highlight or have a badge to show users it has a filter applied. If you hover over it it could ask if you want to keep the filter on or remove it. Second, if you close the layer in the attribute table I think it should at least ask if you want to remove the filter. It should remove selections by default or perhaps ask for that, too. I came upon this idea because after I closed a layer, its selection "ghost" stayed in place. I really didn't expect that and it took me while to figure that out. Thus, dialog prompts will solve this issue.
2. You can't select all. And you can't shift-select past one page of records. This means you can't select more than a dozen or so records. The problem? Say I want to show properties owned by the city by filtering on owner name. Well the layer is scale dependent rendering. To show them all, for purposes of displaying the swath of properties owned across the city, graphically, selection would work fine. However, you can't select them all, to then display, because of this issue. Furthermore, select all and/or shift-select working from top to bottom record, is key, so that you could export all records in a layer with many records. Both shift-select and select all are both key, because shift-select would allow for many but not all records to be selected; also, could be used to remove a swath of records.
3. Exporting many records from a dataset, for example a hundred thousand, does not seem to work. Perhaps that is by design. But I'd recommend a warning dialog in that case rather than it just staying blank. Perhaps they can code it to request it in batches asynchronously from the service to not tie it up?
4. in the future, a second-level select like ArcMap would be nice. This would allow sophisticated re-selection and then re-selection again, to any level imaginable, because since you can sort ascending/descending in any column, that allows you to select a subset repeatedly from a selection.
These ideas would all be useful immediately to a broad audience...