Stuck chasing after the Mad Doctor?  You need to go back and find the Telekinetic plasmid to destroy the large sign that is blocking your path.  There is a room in the Medical Pavilion you need to get into that has ice blocking the door.  The door is in the bottom level below where the path to the doctor.  Once inside you need to find the plasmid and another nice weapon to help you kill the kind doctor.

One of the things I wish I would have done earlier was use the camera more.  By researching Big Daddies, Little Sisters, Splicers, Turrets, Surveillance Camera's and Security bots you gain items to help you defend yourself against them.  You can level up three times and after each time you gain a tonic.  These tonics can be used to increase your defense or make you more elusive.  You also get an achievement when you max out the research on an individual.

Early on hacking is very easy and can be done quickly.  As you progress it becomes much more difficult so you need to apply aids to your gene setup.  You can buy slots in your hacking setup and these will remove some of the difficulty.

If you follow the goal instructions too carefully you will miss important areas of each level.  Take your time and explore each level.  Often you will find nice little treats waiting for you in these areas like weapon upgrade machines or new tonics.

When it comes to harvesting vs rescuing the Little Sisters you have a moral decision to make.  You will gain a lot more Adam by harvesting the Little Sister but then you don't get any rewards for rescuing them either.  The game gives you a 100 point achievement for not harvesting any Little Sister so maybe that will help you decide.  Also the advantage in harvesting is only minor once you get your gifts.