Too much too little time

Your gut feeling is right, that's way too much. Always plan like you're going back. If you were able to make the trip work once, you'll be able to make another one work.

My advice would be to cut out Berlin and Venice. Since Amsterdam and Edinburgh seem like the non-negotiables, do some Amsterdam, then Paris, then London before heading to Edinburgh.

Not sure about the trains, someone else will have to help you with that. Also check out the rail pass area of this website. There is a lot of good information there. I will say that if you're planning on zipping from city to city without seeing much inbetween, then train is the way to go (vs. a rental car).

Holy cow that's way too much! (If you actually want to enjoy yourself, that is.) If you've already booked your tickets to Amsterdam, i'd stick to Amst., London, Paris, and Edinburgh at the most. I'd do Amsterdam - 2, Paris - 4, London - 4, and then finish in Edinburgh. Forget the global pass - it wouldn't be good in Britain anyway. Save money and buy single tickets. Take the train or fly to Paris from Amst.(whichever is cheaper and more convenient for you), the Eurostar to London, then train or plane to Edinburgh. Hopefully you're flying out of Edinburgh, but if not, catch a budget flight back to Amsterdam. Check easyjet.co.uk, ryanair.com, and skyscanner.net for airfare. Flights can be as low as $40 from Amsterdam to Paris, London, Edinburgh.

Unless you enjoy packing, unpacking and checking in and out of lodgings, this plan is WAAAAY too much.
Why not make it easy on yourselves by restricting your travel to places other than those you must be in, to Paris ( a marvelous city)and London? In this, you have the time to relax and savor where you go.
As we have never used a railpass (point-to-point is easier and usually much cheaper), we cannot say whether the pass you suggest is a good choice. If you travel in Britain, yoou will not be able to use Eurail and must use Britrail if you use a pass. too go to Paris,travel by Chunnel train is fast and easy

All the above posters have given you good advice. Yes, it is TOO MUCH!
Definately consider the Amsterdam( x2), Paris( x4), London( x3) Edinburgh( x3) .
Buy your Eurostar tickets online At Eurostar, not RailEurope, ,and do not put down your American address as the Eurostar site then reroutes you to RailEurope and they charge more( I have no idea why). Use your hotel adddress in Paris as yours ( just look on hotel web site, and list address) and then print the online confirmation to pick up tickets at Gare Du Nord, buy a return Paris London ticket even though you will only do Paris - London. One ways cost more usaully. Try to travel on tues, wed. or thurs , as those are " cheaper days" .
I would start on that immediatly as cheapest fares go first. I paid only 45 euros two years ago in summer, BUT, a travel agent here in my town could only quote me fares of 300-400 DOLLARS,, I did my homework though and it paid off.

The title of your post says it all.

In thirteen days I'd pick three destinations--including Edinburgh. So maybe Paris-London-Edinburgh.

Add Amsterdam at the beginning if you are all focused, nimble, like trains, and just want to hit highlights.

Eurail Global would be overkill for the above.

Yvonne,
I also think it's too much. However, IF you're determined to see and do it all...You could do it similar to "speed dating" style. Only pick three highlights in each city. That's how I've done a bit of extra touring while on layover. It's best to divide it up into a couple trips but sometimes that's not possible. Hopefully you will have many more opportunities to cross the pond, to see and do it all...
But if you really do your homework and plan accordingly, you probably could do at least SOME of the destinations you mentioned, but certainly NOT all. It's really a question of "quality" or "quantity". Your choice.

I've traveled all over Germany but am saving Berlin for an "Eastern Europe" tour. It takes a lot of travel time. Cologne and Munich are great German cities that are easier to reach.

Venice is another long trip, but is a jewel and can't be replaced with another destination.

Look hard at your travel time each day. Will you be happy whizzing by Europe while you try to make your hotel reservation for the evening? Night trains with sleepers aren't bad but they really add up.

The Eurail Pass system does not operate in Britain. If you use a Eurailpass and want to minimize train costs, skip London and fly from the continent to Edinburgh. If London is important to you, at least get your train tix way in advance in order to save money. I would go: Amsterdam-Paris-London-Edinburgh. No rail pass. BTW many Brits would fly from London to Edinburgh for the economy and convenience.

Sorry to say, but I agree, that is too much. I just got back from my Munich, Paris and London trip(with 2 days in the Swiss Alps). I had 18 days and it wasn't enough. The 5 days in London was ok, but the 5 in Paris(city only) and the 5 in Munich(plus surrounding areas) was definitely not enough. You would be losing 3(ish) days in travel alone.

You can do those main cities on your list in 13 days but not really by rail. Consider easyjet.com, Ryanair.com, Germanwings.com, TuiFly.com, airberlin.com and others. Berlin, Paris, Venice, Edinburgh, London, Amsterdam are all covered by those low cost carriers.

Those discount/low cost air carriers ARE great, just be prepared for delays, flight changes and cancellations. Ryanair changed our flight times FOUR times in the month before we were to use them. Finally, it was going to be so inconvenient, we cancelled and reworked our plans.

I agree with most everyone - 2-3 destinations would be enough. I tend to "do" one area and stay in a base hotel for a week or so and do day trips to surrounding areas before moving on. We also have a timeshare that exchanges with European destinations so it's nice to have a condo with kitchen, laundry & generous sleeping facilities. We tend to timeshare for a week in a more "rural" location, then head off to the city for a week or so. There's PLENTY to do in London and surrounding areas for a week and ditto for Edinburgh/Scotland. We just got back from a week in the English Lake District (unfortunately you probably need a car to get the most out of it) and a week in London (no car required - in fact, it's a detriment!). We've done similar trips to the Cotswolds, Paris, Greece, etc. I feel like I really get to "connect" with places this way rather than just checking off a country in my "seen it" book.