Has my dentist screwed up my implants? (Photo)

its look good, implants are parallel to each other , and position is also perfect. to see bucco -lingual positioning , CBCT is must.

Looking at the post op x-ray the implant placement looks good.  Possibly something "broke" during the extraction.  This is a common complication.  It looks like you were in good hands and the implants appear to be in a good position for a final restoration.  The tooth anterior (in front of) to the implants has limited bone support and you should discuss options to manage this with your dentist.

It's impossible to tell what, if anything, broke during the procedure looking at that film. The spacing looks good to me. Unless you have a cat-scan post op and can post frames from it, there's not really a way to tell from 2D images what is going on three dimensionally. 

There is no noticeable boney defect around the implants. They look to be perfectly secured except for the first Implant being little too close to the neurovascular bundle ( nerve).

Looking at the images you have provided, the implant position looks ideal with sufficient inter implant and implant - tooth distance. Your concern for the bone breaking also isn't alarming, it might have occurred that while drilling for the implant a small portion of the upper most cortical plate or the alveolar bone might have chipped which is not harming.... instead that lil piece can be used as an bone graft material. Any further chip or breakage would heal back and normal bone formation over a period of time against any uneventful healing. If the implant has achieved good stability integration would also be undoubted. So you should not be alarmed and stay calmly but if there is any discomfort you can see the Implantologist and express your concern.I hope this helps.

The area of where the implants are placed appears to be clean and intactfrom what I can see from the xray you posted.  the implant is not too close to the tooth next to it. If anything it could be a bit closer.  Its my guess that your dentist will most likelybe making you a 3 tooth bridge connected by two implants.  If that is the caseyou are in a good position to have a solid set of teeth on the lower right side ofyour mouth.

A CBCT image is the only way to KNOW, but this looks like a well placed implant at first glance. Even if some bone broke, it likely is clinically insignificant. Bone heals. Implants should be ~2 mm from adjacent teeth.