If the Milllenium Falcon really made the jump to light speed would it destroy the galaxay? The universe? As soon as it hit light speed wouldn’t its mass become infinite and have one hell of a gravitional effect?
*yes I know if is only a movie
No.
Because even gravity depends on time to affect things. If you take a fraction of a second to jump to ‘Ludicous Speed’, you don’t have the time to seriously affect any gravitational fields, except for a brief moment.
Tripler
You really think you can move Ceti Alpha V in the fraction of a second?
Besides, in the Star Wars Universe, ships that are going faster than light are traveling in “hyperspace”, ie, outside of normal space.
Even NASA investigates warp drive. Seriously - if you can warp space around your ship, you can travel at sub-light speeds locally, whilst ending up at your destination in super-luminal time. Sadly, the transporter has been deemed possible, but only with the input of several stars-worth of energy.
Given that amount of power will alos be the “outgo”, its safe to say your destination will be completely fried by the time you got there. 
Perhaps a worse problem with hyperdrive and other methods of travelling faster than light is the violation of causality-
you could end up travelling paths in space time that take you backwards in time,
(especially if used in conjunction with relativistically displaced wormholes)
so that the mass you carry with you will exist twice in the same universe, and you might start a feedback loop of virtual particles which could ultimately destroy the universe if faster-than-light travel became commonplace.
So yes, even if putting the Millenium Falcon into hyperdrive doesn’t use all the energy in the known universe (whch it might), it could be a very dangerous thing.
SF worldbuilding at
http://www.orionsarm.com/main.html
I’ve lost my link, but isn’t that NASA scenario dependent on an outside energy source to create the “bubble” in the first place? The ship would be unable to “warp” by itself…
[Off to search Astronomy and Scientific American]