FYI, it can be a problem installing Linux Mint 17.3 on "newer" (post-2009) SATA HDD that are 250 GB or above in capacity because of newer HDD technology = partitions not properly aligned with the disk. Something to do with 512 bytes data blocks in older IDE/PATA HDD (that came in 120 GB or less sizes) and 4096 bytes data blocks in newer HDD. E.g., the error message during installation = "... offset of 3584 bytes from minimum alignment ...".
If you get this error message during install of Linux Mint 17.3 on an external/USB HDD, you need to first use GParted (which is included in the Live DVD or USB-stick) to realign the modern SATA hard disk, i.e., unmount the HDD (usually is /dev/sdb or /dev/sdc), delete the whole old partition and create the first new partition meant for the "/" or root partition (e.g., 20 GB in size), with 1 MiB (= the default value) at the "beginning of this space""free space preceding" and 0 MiB at the "end of this space""free space following", ensure "MiB" alignment box is checked (= do not select "cylinder"), set it as Primary partition and format to FAT32 file system (= quicker process, i.e., no need to use ext4 yet).
....... When creating the new 2nd partition meant for the home partition (e.g., 30 GB in size), set 0 MiB for both the beginning and end of thisfree space preceding n following, Primary partition and format to FAT32fat32.
....... If you have less than 4 GB of RAM, you can also create a new third partition for swap area (e.g., set as 2 GB in size) for virtual memory/RAM on the hard disk, ... do as for the home partition above.
You can leave the remaining space as unallocated or free space. After the install and boot, you can create a fourth new partition to store your back-ups, movies, music, photos, files or install another Linux distro (= need to sudo update-grub to dual-boot).
Only after partitioning the external HDD with GParted, can you proceed with the Install via the Live DVD or USB-stick. Click "Something else", click the first partition that you had created earlier with GParted, click "Change", click "ext4 file system", click "/" for Mount point, and so on, and also for the /home and swap partitions.
....... Ensure that the device for the bootloader installation is set to the external HDD, e.g., /dev/sdb or /dev/sdc. The cptr's internal HDD/SSD is usually identified as /dev/sda.
Seems the Linux installer does not realign modern SATA HDD when you create a "New Partition Table" for the / (root), /home and swap partitions during the install process.
I have just successfully installed and booted LM 17.3 on a "modern" SATA 250GB external/USB HDD which initially had the above error message about the first root partition not properly aligned with the HDD during install = could not proceed with the install. This was after many hours of reinstalling, trial and error.
....... Previously, I had no problem installing and booting LM 17.3 on an old external IDE/PATA 80GB HDD, i.e., no need to use GParted.