Remember last visit dashboard tab - you need to have more than one Tab on the Dashboard to see the effect.
Below is the screenshot from my Dashboard - as you can see I have several of them. The applets on each Tab should be organized by topic or whatever you like, but in such a way that all applets fit the screen and there is no need to scroll up and down - instead you switch the tab:

But when you go to another module/record - for example after clicking a link from an applet - and you would like to go back to the Dashboard it will default to the first tab, in my case this would be "Outlook". This setting - Remember last visited Dasbhoard Tab - simply let's you return to the tab you had active last time - in my case "To Do".
As for Perspective: this is a general filter that works in some module which can utilize this feature. If the button is grey - it means it will have no effect on the module you are in, for example in Companies. When it is green - it shows the name of current perspective.
The default perspective is "My Records". You can switch to a different one, for example the perspective can be your co-worker. The perspective is active until you switch it. You can also create Presets, for example you can have a Preset named "My Team" and add several users to this list.
How to use it? Let's say one of your co-workers calls in sick and you need to take care of his duties - phone calls, tasks, meeting etc. You just change the perspective - and when you visit the Calendar, Tasks and other modules - you will see this person's records as if it was him/her. This way you can lookup his/her calendar and notify people that he/she will not be able to attend the meeting or send someone instead, check his/her task list etc.
Of course there is a major difference between using the perspective and being logged on as this user. In perspective mode you don't have access to his/her private records (records marked as private) and your permissions apply.