Are you direct sequencing from your PCR product, sequencing in one direction, and using a primer located within your fragment? Your sequence will start several bp downstream of the 3' end of your primer. Try sequencing in both directions and assemble the forward and reverse reads to cover the whole fragment, or clone it into something like TOPO and use the flanking M13 sequences to start your reads outside of your target.
Your issue with the control is likely the physical limitation of Sangar sequencing; 700 bp is a pretty typical read length before the quality drops off. Again, you need to sequence in both directions (sense and anti-sense).
Usually, first sequenced bases are unreadable so you can not cover all of the PCR fragment. You can read the antisense or clone your fragment and sequenced with universal and reverse.
Are you direct sequencing from your PCR product, sequencing in one direction, and using a primer located within your fragment? Your sequence will start several bp downstream of the 3' end of your primer. Try sequencing in both directions and assemble the forward and reverse reads to cover the whole fragment, or clone it into something like TOPO and use the flanking M13 sequences to start your reads outside of your target.
Your issue with the control is likely the physical limitation of Sangar sequencing; 700 bp is a pretty typical read length before the quality drops off. Again, you need to sequence in both directions (sense and anti-sense).
I presume you are using your PCR primers as your sequencing primers. As the other commenters have mentioned, this is perfectly normal. You won't get the primer sequence, only the sequence 3' of it after a few nucleotides (the resolution is generally a little iffy also immediately after the primer) which would explain why your PCR-ed 163 bp sequence seems slightly smaller. Furthermore, you will generally get about 500-800 nt of reliable sequence read from the dye-terminator sequencing (basically the resolution of individual peaks/bands also makes it hard to "call" bases with accuracy after 500-800 nts). That would explain why you could sequence only about 700 bp of your control DNA.
As the other commenters have already mentioned, the solutions to both of these issues are fairly straightforward. To sequence you PCR-ed product, simply clone it into an appropriate vector (the TOPO series of vectors are particularly well suited to this), and sequence using vector specific primers that flank the insert.
If you want to sequence your ~1000 bp long control DNA, either (1) use nested internal primers (say, every 500 nt or so), or (2) if your control is say, a circular plasmid, sequence bidirectionally (both clockwise and anticlockwise) from a starting point, and use the overlap at the 3 prime ends to compile the complete sequence.